340 Demon

To answer the question, yes running too low of an octane fuel will make your engine run hot. As the others here have said, running hot is the least of your worries! You are running hot because of detonation or "pre-ignition". Too low of an octane number means that the fuel has less resistance to fire. This means that the mixture ignites well before the piston reaches it's optimum height in the cylinder. When this happens, the crank is pushing the piston up while the explosion is pushing the piston down. Enough of this, and your piston will break into little pieces.

The additional heat is because every cylinder is firing earlier and causing a lot more friction between the components. At 13.5:1 compression, you need 110 race fuel. Other wise, you'll soon be able to fit all of your pistons in the palm of your hand!