Myth: premium has more power / burns hotter
'premium' is higher octane... the higher octane, the more pressure / heat the fuel can withstand before it ignites spontaneously... takes longer to burn, is more difficult to ignite!
High performance, high compressions engines need higher octane fuel so that the fuel ignite ONLY when it is 'told' to by the spark plugs. Low compression, low performance engines absolutely do not need, and cannot take advantage of high octane fuels. It might even run WORSE if the ignition system is not up to snuff.
A high compressions motor can pre-ignite the fuel if it is not high enough octane. You get 'ping' or 'knock' due to this. The fuel is igniting while the piston it still headed UP, because the fuel ignited too early due to high pressure /heat in the combustion chamber.
A high compression motor can make more power because the benefits of high compression overcome the negatives of hi octane.