Allen wrote:

I was always told the higher octane burns faster, and is consumed in a
shorter duration, thus a lower temperature.

Other way 'round on the burn rate. From a motorcycle performance site -

"The higher the octane, the slower the speed of the burn; the lower the octane
the faster the burn. If the burn is too fast, uncontrolled combustion can
occur. This most often is heard as “pinging” and is commonly referred to as
detonation. This is because instead of burning through top dead center of the
combustion stroke, the entire charge is ignited too early and explodes in the
chamber and acts as a bomb. Conversely, if the speed of the burn is too slow,
it continues after the useful work can be done in the motor and manifests itself
as poor throttle response, reduced power output and increased emissions and fuel
consumption. An engineering fact: THE MOST HORSEPOWER IS MADE AT THE THRESHOLD
OF DETONATION. We have often gained horsepower on the dyno and felt improved
starting and driveability going from Premium grade gas to Regular. This change
was recently quantified in a customer’s Ducati M900 by reducing the cranking
time to start-up from 15 to 3 revolutions, although part of the improvement is
explained below."

George Patterson
Why do men's hearts beat faster, knees get weak, throats become dry,
and they think irrationally when a woman wears leather clothing?
Because she smells like a new truck.