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I have an Energy Plus file with the following warnings in the .err report:

 ** Warning ** Inside surface heat balance did not converge with Max Temp Difference [C] =2.501E-003 vs Max Allowed Temp Diff [C] =2.000E-003
 **   ~~~   **  During Sizing, Environment=SUMMER DESIGN DAY IN UNTITLED (01-01:31-12) JUL, at Simulation time=07/15 15:00 - 15:10
 ** Warning ** Inside surface heat balance did not converge with Max Temp Difference [C] =2.401E-003 vs Max Allowed Temp Diff [C] =2.000E-003
 **   ~~~   **  During Sizing, Environment=SUMMER DESIGN DAY IN UNTITLED (01-01:31-12) JUL, at Simulation time=07/15 17:10 - 17:20
 ** Warning ** Inside surface heat balance did not converge with Max Temp Difference [C] =2.247E-003 vs Max Allowed Temp Diff [C] =2.000E-003
 **   ~~~   **  During Sizing, Environment=SUMMER DESIGN DAY IN UNTITLED (01-01:31-12) AUG, at Simulation time=08/15 15:20 - 15:30

I'm not clear what is indicated by this, if I need to worry about it or not, and if I do need to worry about what I might try to correct the problem.

Additionally, I'm confused that the recurring error summary at the bottom of the .err file says the error occurred zero times during Sizing, but the prior error messages indicate that they occurred during Sizing?

  ************* ===== Recurring Error Summary =====
  ************* The following recurring error messages occurred.
  *************
  *************  ** Warning ** Inside surface heat balance convergence problem continues
  *************  **   ~~~   **   This error occurred 749 total times;
  *************  **   ~~~   **   during Warmup 0 times;
  *************  **   ~~~   **   during Sizing 0 times.
  *************  **   ~~~   **   Max=150.135654 [C]  Min=1.988373E-003 [C]
  *************

I have an Energy Plus file with the following warnings in the .err report:

 ** Warning ** Inside surface heat balance did not converge with Max Temp Difference [C] =2.501E-003 vs Max Allowed Temp Diff [C] =2.000E-003
 **   ~~~   **  During Sizing, Environment=SUMMER DESIGN DAY IN UNTITLED (01-01:31-12) JUL, at Simulation time=07/15 15:00 - 15:10
 ** Warning ** Inside surface heat balance did not converge with Max Temp Difference [C] =2.401E-003 vs Max Allowed Temp Diff [C] =2.000E-003
 **   ~~~   **  During Sizing, Environment=SUMMER DESIGN DAY IN UNTITLED (01-01:31-12) JUL, at Simulation time=07/15 17:10 - 17:20
 ** Warning ** Inside surface heat balance did not converge with Max Temp Difference [C] =2.247E-003 vs Max Allowed Temp Diff [C] =2.000E-003
 **   ~~~   **  During Sizing, Environment=SUMMER DESIGN DAY IN UNTITLED (01-01:31-12) AUG, at Simulation time=08/15 15:20 - 15:30

I'm not clear what is indicated by this, if I need to worry about it or not, and if I do need to worry about it, what I might try to correct the problem.

Additionally, I'm confused that the recurring error summary at the bottom of the .err file says the error occurred zero times during Sizing, but the prior error messages indicate that they occurred during Sizing?

  ************* ===== Recurring Error Summary =====
  ************* The following recurring error messages occurred.
  *************
  *************  ** Warning ** Inside surface heat balance convergence problem continues
  *************  **   ~~~   **   This error occurred 749 total times;
  *************  **   ~~~   **   during Warmup 0 times;
  *************  **   ~~~   **   during Sizing 0 times.
  *************  **   ~~~   **   Max=150.135654 [C]  Min=1.988373E-003 [C]
  *************

I have an Energy Plus file with the following warnings in the .err report:

 ** Warning ** Inside surface heat balance did not converge with Max Temp Difference [C] =2.501E-003 vs Max Allowed Temp Diff [C] =2.000E-003
 **   ~~~   **  During Sizing, Environment=SUMMER DESIGN DAY IN UNTITLED (01-01:31-12) JUL, at Simulation time=07/15 15:00 - 15:10
 ** Warning ** Inside surface heat balance did not converge with Max Temp Difference [C] =2.401E-003 vs Max Allowed Temp Diff [C] =2.000E-003
 **   ~~~   **  During Sizing, Environment=SUMMER DESIGN DAY IN UNTITLED (01-01:31-12) JUL, at Simulation time=07/15 17:10 - 17:20
 ** Warning ** Inside surface heat balance did not converge with Max Temp Difference [C] =2.247E-003 vs Max Allowed Temp Diff [C] =2.000E-003
 **   ~~~   **  During Sizing, Environment=SUMMER DESIGN DAY IN UNTITLED (01-01:31-12) AUG, at Simulation time=08/15 15:20 - 15:30

I'm not clear what is indicated by this, if I need to worry about it or not, and if I do need to worry about it, what I might try to correct the problem.

Additionally, I'm confused that the recurring error summary at the bottom of the .err file says the error occurred zero times during Sizing, but the prior error messages indicate that they occurred during Sizing?

  ************* ===== Recurring Error Summary =====
  ************* The following recurring error messages occurred.
  *************
  *************  ** Warning ** Inside surface heat balance convergence problem continues
  *************  **   ~~~   **   This error occurred 749 total times;
  *************  **   ~~~   **   during Warmup 0 times;
  *************  **   ~~~   **   during Sizing 0 times.
  *************  **   ~~~   **   Max=150.135654 [C]  Min=1.988373E-003 [C]
  *************

I have an Energy Plus file with the following warnings in the .err report:

 ** Warning ** Inside surface heat balance did not converge with Max Temp Difference [C] =2.501E-003 vs Max Allowed Temp Diff [C] =2.000E-003
 **   ~~~   **  During Sizing, Environment=SUMMER DESIGN DAY IN UNTITLED (01-01:31-12) JUL, at Simulation time=07/15 15:00 - 15:10
 ** Warning ** Inside surface heat balance did not converge with Max Temp Difference [C] =2.401E-003 vs Max Allowed Temp Diff [C] =2.000E-003
 **   ~~~   **  During Sizing, Environment=SUMMER DESIGN DAY IN UNTITLED (01-01:31-12) JUL, at Simulation time=07/15 17:10 - 17:20
 ** Warning ** Inside surface heat balance did not converge with Max Temp Difference [C] =2.247E-003 vs Max Allowed Temp Diff [C] =2.000E-003
 **   ~~~   **  During Sizing, Environment=SUMMER DESIGN DAY IN UNTITLED (01-01:31-12) AUG, at Simulation time=08/15 15:20 - 15:30

I'm not clear what is indicated by this, if I need to worry about it or not, and if I do need to worry about it, what I might try to correct the problem.

Additionally, I'm confused that the recurring error summary at the bottom of the .err file says the error occurred zero times during Sizing, but the prior error messages indicate that they occurred during Sizing?

  ************* ===== Recurring Error Summary =====
  ************* The following recurring error messages occurred.
  *************
  *************  ** Warning ** Inside surface heat balance convergence problem continues
  *************  **   ~~~   **   This error occurred 749 total times;
  *************  **   ~~~   **   during Warmup 0 times;
  *************  **   ~~~   **   during Sizing 0 times.
  *************  **   ~~~   **   Max=150.135654 [C]  Min=1.988373E-003 [C]
  *************

Update 3/16/2018: I ran the file with 12 timesteps per hour as suggested in the answer from @Avi. The same errors still occur, and the number of occurrences reported in the error summary actually increased to 1101 times (previously 749 times). What else can I try?

I have an Energy Plus file with the following warnings in the .err report:

 ** Warning ** Inside surface heat balance did not converge with Max Temp Difference [C] =2.501E-003 vs Max Allowed Temp Diff [C] =2.000E-003
 **   ~~~   **  During Sizing, Environment=SUMMER DESIGN DAY IN UNTITLED (01-01:31-12) JUL, at Simulation time=07/15 15:00 - 15:10
 ** Warning ** Inside surface heat balance did not converge with Max Temp Difference [C] =2.401E-003 vs Max Allowed Temp Diff [C] =2.000E-003
 **   ~~~   **  During Sizing, Environment=SUMMER DESIGN DAY IN UNTITLED (01-01:31-12) JUL, at Simulation time=07/15 17:10 - 17:20
 ** Warning ** Inside surface heat balance did not converge with Max Temp Difference [C] =2.247E-003 vs Max Allowed Temp Diff [C] =2.000E-003
 **   ~~~   **  During Sizing, Environment=SUMMER DESIGN DAY IN UNTITLED (01-01:31-12) AUG, at Simulation time=08/15 15:20 - 15:30

I'm not clear what is indicated by this, if I need to worry about it or not, and if I do need to worry about it, what I might try to correct the problem.

Additionally, I'm confused that the recurring error summary at the bottom of the .err file says the error occurred zero times during Sizing, but the prior error messages indicate that they occurred during Sizing?

  ************* ===== Recurring Error Summary =====
  ************* The following recurring error messages occurred.
  *************
  *************  ** Warning ** Inside surface heat balance convergence problem continues
  *************  **   ~~~   **   This error occurred 749 total times;
  *************  **   ~~~   **   during Warmup 0 times;
  *************  **   ~~~   **   during Sizing 0 times.
  *************  **   ~~~   **   Max=150.135654 [C]  Min=1.988373E-003 [C]
  *************

Update 3/16/2018: I ran the file with 12 timesteps per hour as suggested in the answer from @Avi. The same errors still occur, and the number of occurrences reported in the error summary actually increased to 1101 times (previously 749 times). What else can I try?