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At the bottom of your first graph is when the zone temperature has become cold enough to turn on the furnace in your EMS program, so the furnace heating input is quickly raising the zone temperature. At the top of your first graph is when the zone temperature has become hot enough to turn off the furnace in your EMS program, and so removing the furnace heating input quickly cools down the zone. Even though you don't have cooling equipment, the zone temperature might drop that quickly because this is January and it's very cold outside. If you were to look at a summer day instead, you would likely see different zone temperature behavior.

Extending your thermostat deadband would cause less periods where the action changes, but you would still see this quick change in zone temperature for January during the timesteps when the action does change.