Jim W:

Go to the outlet nearest the dead one, that does work. After turning the power off, you can open it and inspect it for a broken or loose connection. If here is no obvious fault in that outlet, open the one that is dead and inspect it. Either of these locations is a likely location for the failure. Also check that all GFCI are operating, sometimes they will protect several outlets and if it has been tripped or tested and not reset it could cause the problem you describe. You will need some type of test equipment to do this and a screwdriver. The heater operating has nothing to do with the outlets, they are on two different circuits and voltages.
If this does not solve the problem, you need to call a qualified professional electrician.

bboppalou:

Danger. If you feel confident using metal tools around electricity, proceed. Use common sense. If you have ANY doubt about what you find, see, observe, learn, then bite the bullet and call somebody. The problem is very likely just what you say, a small problem. But, if you do not have the experience in manufacture with electrical circuitry, you may make the problem worse, while jeopradizing physically in the process.