I've got a single Dometic heat pump and my manual says that when the outside temp reaches 40º the compressor will shut down and will not run again until the ambient temp reaches 45º or better. When it's somewhere near that temp, my fan turns off with the compressor still running and stays that way for 5-10 minutes before the fan comes back on. My guess is that the unit is running the compressor to heat the freon as much as it can before any heat is extracted. I turn on a couple of electric heaters when the temp is going to drop into the 30's. Even with those operating quirks I still like mine quite a bit.
"If you come to a fork in the road, take it."
Austin, TX "Rancho Deluxe"