Heat pump runs constantly. It will shut off for about 4 minutes then restart again. Temps have been 40's for the high and 20's for the low.. The heat pump seems to be running a lot more than normal for the temps to be this warm. Any suggestions?

Sounds like you are maxed out on the efficiency of your heat pump. Where do you live? Typically, heat pumps are not the favored choice in USDA zones 6 or colder. I live in the Atlanta area and even here heat pumps are rare. You might look at Geothermal Heat Pumps if you are in a colder area.