you do know the octane rating on fuel is its resistance to burn right. it has absolutely no bearing on how hot the fuel runs. it literally just means it harder to ignite at high pressure. which is why higher octanes have to be run in high performance engines.
which is why it is recomended to run higher octane in small engines due to the fact that regular can ignite pre maturely under high temp/high compression applications. thus causing engine damage to smaller weaker components in small engines. 93 octane is designed to not ignite before the spark plug actually ignites it. while in certain situations 87 can self ignite durring compression.