Has anyone tried replacing the radiator cap? This inexpensive part is often overlooked as a source of cooling problems. I’d buy one from the local parts store and see if it makes a difference.
You may be cooking yourself for nothing. Perhaps the heater is not what’s bringing the engine temperature down. Maybe the thermostat and fans are doing it, and it’s coincidental that it happens as you play with the heater and blower.
Maybe the new thermostat opens at a higher temperature than the old one (not the faulty one) and that’s why the gauge is moving higher now. Once it opens, however, the gauge should stop moving around and stay in one place.
Maybe you got a second faulty thermostat.
We still have to verify correct operation of the cooling fans.
The outside temperature may have nothing to do with this problem. It seems to be less and less relevant as time goes on.
If this were my car I’d start it, open the hood, let it idle, and watch to see what happens. No heat, no blower, no nothing. Watch the gauge, feel the radiator so you know the thermostat is opening, and watch the fans. The fans should come on before the gauge reaches the red. Long before, actually.
If the radiator does not boil over, the engine is not overheating. It may be getting slightly hotter than before, but that’s not the same as overheating.