Sounds fishy, A/C amplifier is only to do with A/C and to switch the fans in series and low speed.
If you disconnect the sender on the radiator fans should come on by default.
If the gauge goes up in temp its on the outlet to the left of the radiator passenger side. The sender is on the right drivers side.
I reckon the guy who sold you this car really knows whats wrong :(
Feel the hose on the right and see if its hot. If it isnt its not circulating .