1) A connection in the wall outlet is loose. A loose connection produces heat, because the gap inside the connection forms an arc that causes sparks.
2) You may have a loose connection somewhere else in the electric circuit. Heat can travel through the wires from another location in the circuit to the wall outlet. Does the breaker box feel too warm?
3) You may have a loose connection inside the kiln switch box. Heat from that connection may travel through the cord to the wall outlet.
4) Does your kiln have the original factory cord set? If you replace the cord with a smaller one, you will definitely burn up a wall outlet. The common dryer cord is especially notorious for burning up wall outlets. Replacing the cord on a kiln voids the warranty and may void the kiln’s UL Listing.
5) Is the circuit wire (the wires that run between the circuit breaker and the wall outlet) of proper size? Wire that is too small will burn up the wall outlet.
6) Do you have aluminum wire in the circuit? If so, you must use a special paste when connecting aluminum to a copper connection. I suggest replacing aluminum wire with copper.
7) Frequently plugging and unplugging heavy-amperage cords will weaken the wall outlet. When the plug is easy to insert into the outlet, the outlet is too loose. This, in turn, will produce heat in the outlet.
8) The cord should hang down loosely from the wall outlet. If the kiln is too far away and the cord is pulled to one side or the other, the cord may twist the plug in the wall outlet. This can cause the outlet to fail eventually.