Our heat pump system's ductwork is very well sealed and insulated, including the plenums. It's on a digital timer thermostat and we never touch it when the stove is going. If heat is required it comes on. Normally this doesn't happen when the stove has been running a while, but if it does no big deal. Well designed and properly installed heat pump systems often will work better for heat distribution because they are designed to distribute lower temperature air than a oil/gas furnace system. That said, every house is different. Many installations are low budget or the installer cut corners. If so the results may be less satisfying.
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