Check the thermostat and the heater core if its clogged, and also the air blend door could be stuck in the cold position

A bad heater core should not make the car run hot. If coolant is
not circulating in the cooling system, then the heater core will
not receive any warm coolant... which will result in NO heat inside
the vehicle.

If the water pump belt is broken, then the engine will run hot and
you will not have any heat inside (because no coolant is circulating).

If the belt is on the water pump, it could be a faulty pump impeller.

Some pumps have plastic impellers that break... resulting in no
circulation of coolant.

A stuck closed thermostat will also cause the engine to run hot... but
you would still get heat inside the car, because coolant is still
able to circulate (as long as the water pump is working).