If I understand:
- New radiator
- New radiator cap
- New Thermostat
Guessing these new parts were installed to CURE overheating problem you were already having?
First - is the cooling system full? Sometimes they need to be "burped" to get any air out.
I've had almost new thermostats fail for no reason whatsoever, could be bad, out of the box.
If thermostat is easy to get to, you can check basic operation (open, close) in boiling water on the stove.
If you have right kind of cooking thermometer, you can check for open/close at correct temperature
When does the car overheat, in traffic, or at speed?
You noted that the fans turn on, but do they
stay on?
You might try bypassing the switch that controls them - so that they stay on indefinitely - and see what happens.
If none of these, I'd think water pump, but first, have someone check for combustion gases in coolant - that would indicate a bad head gasket.
Good Luck