overheating m42 95

[alray]

history:
coolant was old rusty water pump was weeping.
bought radiator flushes x 3 hoping to clean it before pump went.
removed thermostat it was badly corroded, new oem housing gasket.
pump went and destroyed belts both of them.
had to remove the pump in pieces it was rust welded as well as plastic impeller destroyed.
cracked housing on the long bolt as I used it to drive pump in.
used the timing chain cover bolt to drive in the pump into the engine then replaced bolts with regular ones.
one last radiator flush and filled with distilled water and mocool.
no water leaks and or air bubbles in the rad.
today I found out :
heats up when not moving.
while parked cools off when accelerated hard.
fan only works when a/c is on.

so far from what I have read im going to change the purple relay but...
if I have a/c on all the time so the fan is working all the time why is it overheating. further more if the thermostat is gone shouldn't it run cooler?
cooler by miami weather i expected a few degrees not much never overheating....

thanks for any help.