[Padgett]

Running a higher octane than the vehicle requires does nothing at best and can reduce economy & power, and make the engine run hotter

As far as power, high test has the same BTU/lb as regular. What higher octanes have is extra refining and additives to make the gasoline burn slower (avoid detonation/autoignition) but in order to extract the same power, the timing needs to be advanced. Not all computer cars can do this.

If not the timing is effectively retarded, and you need more gas to make the same power which raises the engine temps.

OTOH if the computer is designed to advance the timing accordingly, you could see an increase in power/mpg particularly if the engine has a compression ratio above 10:1 or if you have boost.

Otherwise no. I just use what the manufacturer recommends.