Before changing anything, do the logical checks:
Assuming it is an old tech wax expansion type, put it the thermostat in boiling water to see if it opens , also check the fan is switching on. If any of the cooling system is controlled by electronic sensors, try an OBD2 diagnostic test.
If those are ok, flush out the radiator just in case the waterways are blocked.
Finally pressure test the cap and the system at the filler, preferably when the coolant is warm. If that is all ok sounds like a blown head gasket, unfortunately .