"However, if there is much more than I need on the coldest clear winter days, then I should use it, no? The most efficient way would be to blow the air directly during the daylight hours, as you said. But what if every time the house gets too hot and the thermostat turns it off or directs the hot air outside it instead directs that extra hot air to a heat exchanger that heats water for later. That makes sense to me."
That makes more sense to me now that you've worded it that way. Keep us posted.