The first thing to check for is if there’s air trapped in the cooling system. This can cause the no heat problem and if there’s air in the location of the coolant temp sensor for the radiator fan the fan won’t turn on. Coolant temp sensors don’t read air temperature.
With the engine cold, look on the engine for an air bleed port for the cooling system. Open the port and add coolant until all the air is purged from the cooling system and where nothing but coolant comes out of the port. Then close the port.
Tester