I doubt the hair dryer is drawing too much current. The most likely reason is that there is a poor connection somewhere near the prongs. The resulting resistance creates a heat producer, just like any resistor. So, where is the bad connection? It could be oxidation on the surface of the prongs, or the surfaces of the metal inside the slots they plug into. I could also be inside the moulded plug body, with worn wires that have partly broken off leaving few strands to carry the heavy current. The heat is actually generated at the worn-out wire site, but it is conducted by the wires and the metal prongs out to where you can touch them. I have seen this phenomenon in a different way - the plug body itself seems very warm when you go to grab it to unplug. Solution for this? Replace the plug on the end of the cord, maybe cutting a few inches of cord off with the old plug. The frayed wires inside may be just outside the plug body, where the cord gets flexed often as it is handled normally.