Perhaps a good start would be to mention what make/model/year car
you're talking about.

Leaving the electric fan on when the water pump has stopped does little
to cool the engine.  If the engine is stopped, it won't get any hotter.
Many automotive engineers consider the benefits to be less than the
risk of running the battery down.

What mix of antifreeze are you using?  100% antifreeze won't cool
as well as a 50/50 mix and offers no benefit over 50/50.
How old is the radiator?
How hot is the engine running?  Is "high heat" a bit hot, or boiling
over?  If boiling over, then you might have installed the thermostat
backwards.
Any signs of slippage on belt to the water pump?