A 1500 watt heater is slightly too large for the common 15 amp circuit wired up with #14 wire in your house. Understand, the bigger the number, the smaller the wire. Even if it is a 15 amp circuit, the voltage drop isn't going to be very much, and would actually result in the heater drawing slightly lower power. I doubt the house wiring has anything to with it. I am a little disturbed the heater cord itself is heating up. Does it have a label on it?
I have a couple of the heavy duty cords mean for window A/C units, but neither is marked with its size. I am sure it would at least be on the packaging at the store.
Is the heater plug OK? If it is blackened, just scrape the black off. If part of it is burned away, better replace it.
Listen to what tkrussell said about not unplugging things when they are on. Actually, listen to everything he said.
The biggest problem with 40 year old wiring is that it may not have the ground you need for 3 prong plugs to protect you the way they should.
