Waterpump pumps the coolant around, radiator cools it and thermostat 'regulates' the Flow of water by opening more when the coolant gets hotter with a maximum opening at +- 88°?
My guess is that the previous thermostat was opening too soon/too quick thus cooling too much, toghether with the alloy rad that, for a given opening of the thermostat, cools More than the copper rad where the thermostat was designed for (maybe an alloy rad needs a Different thermostat calibration)?
So the water cooled too much => thermostat closed => heats up and repeat, like The thermostat is almost bouncing ?
Or am I overthinking?
I'm sure (hoping for your sake) that's just a loose draft,,,,,