again, no such thing as a heater motor, it's called a blower motor. and no, the blower motor being bad is not going to do that. all car gets there interior heat from the heater core. in front of that heater core is a door that opens and close and directs the air flow. more then likely, the problem is the door is stuck open and the air is blowing across the heater core, causing hot air to come out of the vents.

Nope. When the heater motor goes bad, it either makes a lot of noise or doesn't move any air around. It sounds like you have a problem with one of the doors that direct the air.

If your question is, should hot air come out of vents or dash when heater is off. the answer is no. If you still feel hot air then your have a actuator or heater door stuck open.

but if your question is should the blower motor still blow air out vents or dash when turned off then read below.

most HVAC system on cars have a module or controller for the blower motor.

Blower motor 101, class in session....

Blower motors only have one speed, however there is a blower module or control on or near the blower case. this device it what lets the driver change the speed of the blower motor.

When this part fails the blower only blow on high speed which techically is the only speed the blower has.

good luck, you can find this part at AutoZone for about 20-40 bucks

Yep, air door is stuck open. Cable from dash lever to air door broken or dis-connected most likely.

No, if the motor is bad it would either not run or be really noisy.. if it runs all the time then you have a short

this has the electronic climate control, yes? edit* good old delphi electronics would be my guess.

Can I have more info on this?