I don't know specific model for a heat pump, but there are Honeywell
electronic thermostats that learn their anticipation (comparing rate of
change of air and wall temperature) and usually hold the temperature
fairly evenly (model CT3500 usually varies less than 1 degree F even for
my steam heat). It can be set for different number of cycles/hr depending
upon type of heat. It only overshoots slightly temporarily if we get
sudden mild weather following cold weather.
My previous thermostat (another brand) had minimum +-1F setting and no
anticipator. It would drop -1F below setting, fire to +1F above setting,
and continue to climb due to hot radiators (3-4F swing).
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