Re 'at higher temperatures the volume of fuel is less'
I think Mainframe may have had one Crownie above gross. Perhaps he had it hot in order to get more volume for the same weight. I think he meant that at higher temperatures the weight is less for a given volume of fuel.
Re fuel, my experience with an IO520 Continental has been that when I operate in cold places with cold fuel I require a higher fuel flow for my usual power settings. I'm probably getting more power but I need it to push through the cold dense air. In hot climates I can run further lean of peak (probably due to better atomization of the the hot fuel in the hot intake air) . My indicated airspeed is down slightly but my TAS is just as good if not better than it is when flying in cold air. I may have been dudded in the amount of energy I purchased (high volume low weight) but it balances out by the more efficient use of the hot fuel in hot air.
Cheers RA
PS We used to use the principle of better atomization in hot air in a Comanche I flew long ago. In cruise we used to operate partial carby heat which gave us smoother operation and better economy.