First troubleshooting step I would take would be to see if the radiator fan power supply wires have voltage at the fan relay terminals while the fans are running. If yes, then I would suspect a shorted connection somewhere. If no, then I would suspect a rewiring job. Next I would pull the heater blower fuse/relay as it sounds like radiator fan operation is simultaneous with heater blower operation. That circuit might be the source of the power.
And yeah, it sounds like a problem with the thermostat. If you could cool an engine by just blowing air over the surface there would be no need for a radiator.