<<The heater circuit is independent of the thermostat, while the
radiator is not. Turning on the heater fans bringing the temp down can
also indicate a bad thermostat. Cheaper and easier to replace than a
radiator. Probably better to start there.>>

Yes and No.

The heater core's are within the coolant loop when the valves are open.

If the thermostst was stuck closed, turning on the fan motor's wouldn't
drop the operating temps any.

It would stay hot.

Seeing as the temp's fluctuate on the gauge depending if the AC is on or
not, I'd bet the raditaor is half plugged.

One question.
Who would drop a new engine in a vehicle without updating the cooling
system ?

I sure wouldn't, and chance frying it.