Higher octane burns faster and hotter
You are partially correct, but mistaken overall.
Higher octane burns slower, and is less likely to detonate under high compression. I don't know if the higher octane actually produces more heat, but the faster detonation times of the lower octane fuels cause more heat to be retained by the cylinder, and this leads to shorter engine life.
Because the higher octane fuels burn slower, they are delivering more energy to the piston (and crankshaft) since they continue to burn closer to the bottom of the stroke. Detonation causes a loss of delivered energy and more retained heat. Alcohol raises the "octane level" because it slows down the combustion and prevents detonation much like fuel with more octane in it.
What alcohol/fuel doesn't do is have as much chemical energy contained within the fuel, so you won't be able to get as much power out of the alcohol enriched fuel.