I have a heat pump with electric Aux.

When outside air temp falls below 35 deg, the compressor almost runs continuously trying to reach set point. The Aux heat wouldn't activate until the room temp falls 2 -3 deg below set point.

This scenario makes for rather uncomfortable temp swings

I would like to find a thermostat that has an adjustable timing algorithm which will kick in the Aux heat if the heat pump does not reach set point within the specified time.

I believe that turning on Aux heat for a few minutes would not be too much more expensive then the wear and tear and cost of the heat pump when approaching 100% duty cycle. This is especially true since I previously was on 100% electric heat.

Most heat pumps are all out at 35 degrees.

Look at the Honeywell programmable selection in the link below and see what you can find that will suit your need.

Default - Honeywell Environmental And Combustion Controls

Look under select home products. Then thermostats.