I don't blame you for being nervous. You might try using it on a different receptacle just to make sure the receptacle isn't part of the problem, but I doubt it is. All I can tell you is what I would do...and that's file that heater in the ol' round file cabinet.

The receptacle is usually the problem. Less expensive and/or older receptacles lose some of the spring tension that hold the plug in. This loose fit causes arcing and heating of the plug and wire. I have seem some that melt the plug completely. Move it to another receptacle or replace the one you are using.

Thanks guys! I had it plugged into a surge protector power strip that also had my computer on it. It tripped the power strip and my computer and heater shut off. It worked fine for about a half hour then shut off. It did what it was supposed to do. Really shouldn't have had my computer on the same strip as the heater, but it's fine. When I surge protector does that it's toast, or can you use it again?

The insulation used on power cords often has a higher temperature rating than typical permanent wiring.
This allows the use of smaller conductors, and for a heater does not even change the efficiency (any heat missing from the heating elements is radiated from the cord).

A loose receptacle can cause excessive heating.
There is ALWAYS some additional heating from a receptacle though.
The resistance of the connection is not zero, and even a few tens of milli-ohms at 10-15 amps causes heating.

If the entire cord is slightly warm it is probably fine.
If the cord cap is slightly warmer it is also likely OK.
If the cord cap is a lot warmer check the receptacle.