My home furnace is currently controlled by a programmable Honeywell thermostat, but it regularly thrashes the furnace by turning the furnace on for just ten or twenty seconds.
It seems that the thermostat will register a one-degree drop in temperature for a few seconds, turning the furnace on, but then switch back up to the previous temperature a few seconds later, turning the furnace off again. Presumably, air currents near the thermostat produce rapid swings in temperature of around one degree.
After some investigation online, it seem that what I need is a thermostat that supports "variable swing" or "deadband" -- that is, heat to a given temperature (e.g. 25 degrees), then let the temperature cool to a different temperature (e.g. 22 degrees). Apparently Honeywell thermostats do not support this.
Which thermostats allow a temperature range to be programmed? I don't want to spend hundreds of dollars on a smart thermostat; a simple and cheap programmable thermostat would be ideal.
Update: the thermostat is a Honeywell Pro TH4000 series, most likely a TH4110D.