I don't think that higher octane will result in a hotter burn. If anything it will result in a cooler, or at least slower, burn. Octane ratings are a measure of a fuel's resistance to detonation. The higher the octane, the less likely you are to have detonation. That's why higher octane allows you to have a higher compression ratio and advanced ignition timing. Before computers, using a low-octane fuel in a motor designed for high octane resulted in detonation, often called knocking or pinging. These days, if you put 87 octane through a motor designed for 93 octane, the knock sensor will pick up the detonation and cause the computer to retard the timing. This all happens without the driver hearing anything. I'm not sure what the motor does when you put 93 octane through a motor designed for 87.