What makes you think it is overheating ?, don't go by the very inaccurate gauge fitted to these.
Radiator thermostat ?, I assume you mean fan switch.
The fan circuit is dead simple, and unfortunately dead shit tbh.
If bridging the switch contacts show a fan/s working you know the switch is ok.
The thing you need to do is to first rewire the whole circuit, by using the original ford fan wiring and fuse, you are risking potentially a fire at worst, or a melted engine.
The fans only come on when sat idling for a long period.
It's not even worth trying to sort out the crap wiring ford put on these for fan control, rewire using the switch to switch another relay with a seperate loom for the fans, either buy one of diy your own, very easy.
tabetha