Could be one of two things, that I can think of.

1. The motor has two centrifugal switches on it. One of them is for the heater, it is supposed to cut power to the heater when the motor stops, perhaps it's contacts are welded together. It is the one with the heavy red wires.

2. This is the more likely, a grounded element. Sometimes the element can sag or break and touch the case, depending how it does this it can give the symptom you describe. You may be able to see this by inspecting the heater assembly. Best way is to check it with a meter.
Unplug the unit.
Remove both wires from the heater and measure it, usually around 10 ohms.
Then measure from each side/connector of the heating coil to the case/frame, both should be infinite ohms (open).
If not you have a grounded element.