Find the temperature sensor, and be sure it was not knocked loose during the move. The next step would be to insulate it. If it is in contact with the heater housing, wrap that with some pipe insulation and cap with vinyl tape.
If it is in a dry (or wet) well in the tub itself, buy a can of spray foam and coat the area around the sensor.
I say all this because it sounds to me as if the sensor is cooling off once the pump stops. That can happen if the sensor is not protected from the outside air- and things such as a poorly-fitting equipment compartment door or some missing siding can add to the problem.
This is an easy fix, and if it doesn't help I would look at the control system next.