I am aware of the adjustable differential setting which is basically a dead band that the room temp can swing through.

I guess I am not explaining the situation clear enough.

I am looking for a timing adjustment for the on time of the heat pump before the thermostat calls for Aux heat. Say 10 minutes or so. If the outside air is in a range or 40 -35 deg, the compressor will never achieve set point in which case, it will run at almost 100% duty cycle.

It seems logical, in this instance, to ask for Aux heat to more readily reach set point without waiting for the -1 or 2 deg drop in room temp before the thermostat as for Aux heat.

Maybe I am asking for something in a thermostat that is readily not available.