I live in a 2 story (plus basement) single family home and am trying to determine the most efficient (energy and cost) way to heat my home in cold weather. I have 2 heating/cooling zones - a gas furnace which heats the basement and first floor, and heat pump for the 2nd floor, where the bedrooms are. At night I typically turn down the furnace and turn up the heat pump thermostat - and do the opposite during the day. On most cold nights the auxiliary heat runs for much of the night. Am I better off keeping the furnace running more so the gas heat rises and takes some load off of the heat pump, or is it best to just let the auxiliary heat do it's job and save the gas?

Every home is different and there is no set rule except to say that gas is usually cheaper than running the auxilery heat.

If you post your NG and KWH costs including taxes, the AFUE of your furnace and SEER/HSPF of your heat pump I can reply with some calculations that will give you a ballpark. In some locales different heat sources have such as discrepancy that sometimes one is significantly cheaper.