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Actually, there is a default for these convergence criteria. From the idd file, the convergence tolerance defaults are 0.04 and 0.4 for loads and temperature, respectively.

 N2 , \field Loads Convergence Tolerance Value
   \note Loads Convergence Tolerance Value is a fraction of load
   \type real
   \minimum> 0.0
   \maximum .5
   \default .04
 N3 , \field Temperature Convergence Tolerance Value
   \units deltaC
   \type real
   \minimum> 0.0
   \maximum .5
   \default .4

The use of 0.005 is not wrong, it's just very tight and would likely be met in most simulations. Changing the temperature convergence tolerance to 0.25 will eliminate these warnings.

What this tolerance looks at is the maximum temperature difference between warmup days. When all convergence tolerances are reached during warmup, the simulation will move on to the actual simulation (unless a minimum number of warmup days is specified).

The question is why did this simulation result in a large difference between one warmup day and another. You could investigate the reason by adding OutputDiagnostics:ReportDuringWarmup to your input file and plotting the zone temperatures for each warmup day. Look for a cyclic change in zone temperatures where every other day is the same, while days in between are different.

For example, if zone humidity control is specified, the warmup may use humidity control on one day, and then find that humidity control is not required on the following warmup day. Then humidity control is required again on the 3rd warmup day and the cycle repeats.

It's not a bad thing that the simulation did not find a very tight convergence solution, it's just that the simulation will proceed with these warmup results. Even a 0.2C temperature convergence is reasonable. For those simulations that cannot converge using a 0.5C criteria, one should certainly determine why that maximum criteria could not be met using the ReportDuringWarmup technique described above.