Here is the wiring diagram
http://www.servicematters.com/docs/wiring/Wiring%20Sheet%20-%203401724.pdf

You will see a centrifugal switch on the motor. This switch should disconnect the heater when the motor is at rest. It ensures that there is no heating without air flow.

Your unit had heat with the motor stopped so there is a problem.
It could be that the switch is staying activated or it's contacts are welded together.

A more likely cause of this is a grounded element.
The element either sags or breaks and touches the case.
It then heats from one side of the line (120 volts) to Neutral instead of across both lines (240 volts)
Depending how it grounds it can do a lot of weird things.

The way to check it is unplug the unit, unplug both sides of the heater and measure it with a meter. Should be 10 ohms approximately. Then measure from each side to the case/frame, both should be infinite ohms (open)

If you do not own a meter, I would suggest you purchase a one. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.

There is a good STICKY at the start of this forum about it's use.