Why would the clothes dryer outlet heat up?

Answer 1

Loose connection, bad connection, they're are a few things that can be wrong. Shut the power down and open that up and check it out. The connection might be heating up. If that looks like the case, cut back and restripp the wires so you'll get a nice clean connection and install a new outlet. If everything looks good then consult an electrition because a dryer outlet can be a little warm but definately not hot.

Answer 2

The usual reason for wires heating up is that they are sized too small for the current the load is demanding. Dryers are fed with #10 wire rated at 30 amps with a 30 amp breaker at the house panel end. Wire smaller that this, #12 or #14 will definitely heat up to a point where the insulation could melt off and the wires short out. Get a qualified electrician to check on this condition before something drastic happens.