Heater wont quit heating , even in off position

Maybe your fan motor has quit working ,but first check your fuses

Fan is working,did you do any work on cooling and heating.

if your heater constantly blows cold then there is a problem with water circulation I:e the heater has a small radiator like your engine has a large radiator the small heater radiator is called a matrix instead of just cooling the water passing through it like the radiator for your engine it is designed to give heat via a fan that blows through it so when it fills with hot water from the engine bay the blower fan blows through it thus giving heat inside the car if it is blowing cold then there is no water getting to it or the water is low in engine bay or there is a blockage even possibly a leak or quite simply the switch that controls the flaps to give you hot or cold air is stuck in the cold position with out more info and me asking more questions this is the basic idea of how it works
hope this helps

Check your blower motor resister,it's next to the blower.

A common problem with seat heaters is broken heater elements. If you can get access to the connections you can check them with an ohm-meter to see if you have continuity or an open circuit.

Have you checked the heater water valve for proper action? If it is in the off position, water won't flow thru the heater core. It may be cable actuated or vacuum actuated.

Your heater box has an arm that opens the door flap to the actual heater core and this can be closed manually if you remove your glovebox and push it by hand. The other part is vacuum operated and is usually located on the top heater hose under the hood as it connects to the heater box. This vacuum operated shutoff can also be manually adjusted to the closed position and locked down until you can locate a new one.

Replace your heater control valve, its the device that channels hot water either around your engine only or when the valve opens it channels it through your cabin also..
They are quite common to fail on pre02 cars...
if all your electrics are ok, and the car is running normal temps, try feeling the pipes around the valve.. its located behind radiator left side looking down.. could even check all related fuses, just to be sure..
Good luck

Swap it with a relay you know to be good and see if it works again,pick a relay that is not important to the function of your car.

Does it have knobs for control or is this Automatic temp control?