Regular, premium is just throwing money away. The engine is designed to run on regular.
Whilst what you say is correct Cliffy, it's not as clear cut as that and speedandstyle makes a good point. We are talking here about putting higher octane fuel in an engine that doesn't need it and that wasn't designed for it. Under those circumstances it's proven that too high an octane fuel will burn too slowly for that engine compared to using it's "designed for fuel", and can damage the exhaust valves and seats. Under those circumstances an engine will produce less power as some of the charge is then wasted, since it's still burning as it exits the combustion chamber. You can see this effect on the dyno and in the lab engines when making any comparison with these fuels in a particular engine that's not designed to run on higher octane. On many of these engines the fuel and ignition maps won't adapt enough to make full use of the higher octane fuels so the fuel is still burning on exit from the chambers. Here is the uk there has been much publicised about this effect, especially on programs like 'Top Gear' etc where they tested differing fuels. As you will know the higher octane fuels explode/ignite in a more controlled way causing the combustion flame to spread more slowly than the violently igniting lower octane fuels (which can cause the knock we all despise). It also requires more energy to ignite higher octane fuel and it won't be detonated by high combustion temperature prematurely, thus avoiding the dreaded knock or pinging which can be so damaging to modern engines. But it requires the engine to adapt too to get the best out of it. On the majority of engines not designed for higher octane fuels we don't build in much adaption/allowance for running on anything more than the octane rating the engine was designed for. There is little point. Therefore the higher octane fuels are not only a waste but potentially, depending on the engine, harmful if used long term. Whilst you can still put in a higher octane you won't get the best out of it and if you continue to run on higher octane, the engine over time may be damaged, and at the very least will suffer from exhaust valve and seat carboning. This is a known phenomenon that occurs to our Burgmans, especially the 400's.
Regarding the running hot or cold issue, this too can be a problem of using the wrong octane fuels. Sometimes this may be evident on the engine temp gauge but usually not. Using a too low an octane fuel is normally a cause in a higher performing engine, of cylinder, head and valves overheating. You will often find the combustion chambers become too hot and this will cause the engine to 'overrun' or suffer from pre-ignition after switching off the ignition. The engine just wont stop on demand with the engine dieseling all on it's own with the engine switched off! This is on mostly carb engines where fuel flow is not cut in the same way or as definitively as injected motors. However, the top half of the engines even on injected motors will run hotter and is measurable. Also of course, the dreaded pinging can take place due to increased combustion temperatures just before ignition. Higher octane will stop all that from happening and allow the motor to run cooler (at it's designed temperature) internally.
So although the fuels themselves don't burn hotter, the ensuing problems of using a fuel that is too low in octane rating will cause the motor internals to heat up more than usual because of combustion irregularities.