I doubt it's the pump, the pump is just a mechanical thing, not too many points of failure. I also doubt it's the radiator, I also don't see too many points of failure, it's either its blocked or it's fine.
I would stand firm on suspecting the CTS and it's wiring or the thermostat. You can remove the wiring and see if the fan runs at full speed, or if the computer is not intelligent enough you may need to short the wiring.
The hot and cold pipes makes me think it could also be a thermostat, you can also remove it and see how the car behaves, I've had a couple fail prematurely.