And let's remember our basic organic chemistry.
Back in World War II, in the quest for ever greater performance, basic physics tells us that performance is limited by the absolute temperature difference between the hot and cold reservoirs. So the push was on to have better metallurgy that could withstand *higher* temperature and pressures, and concomitantly, fuel was required that could withstand the higher temperature and pressure before intentional ignition.
Chemists delivered on these needs with longer chained hydrocarbons, branched chained hydrocarbons, and the infamous tetraethyl lead discovered to delay the onset of detonation.
Octane ratings reached 140, permitting 36 cylinder motors with two stage turbocharging to exceed 3,000 hp normal rating, and upwards of 4,000 hp in emergency rating. These fuels have all but been phased out, and virtually all aviation fuel today (for reciprocating engines) is 100 LL (low-lead).
Higher octane fuel is more expensive, because those extra carbon atoms means there are fewer gallons of higher octane fuel from a barrel of oil, than lower octane fuel.
To this day, a pilot of a piston engined airplane will adjust the fuel/air mixture on the fly based on the exhaust gas temperature gage - at the lower end of the range, the mixture is richer and can produce more power. At the upper end of the range, the mixture is leaner, to greatly extend the range.
So just the opposite, for a motor designed to produce greater power by forcing more fuel into a smaller space, it will run hotter - not cooler.