There are a few reasons to control the temperature of fuel, and very seldom does it have to do with outright power.
First off, optimal fuel temp can increase combustion efficiency but the effect is typically <1%.
Second, there are different factors at play with aviation applications and automotive.
The real answer is it is vehicle specific. Understand there is FAR more air than fuel in the combustion chamber at any given time so the density of the charge is rarely a concern with the gas, that's an air concern. Also, consider that the specific heat of gasoline is relatively low, so whatever heating/cooling is done can be changed quite easily making it a difficult/futile endeavor.
So anyway, in aviation, turbine engines have no predetonation issues to contend with and warmer fuel DOES atomize better, thus (and in combination with the issue of frigid temps at altitude) you will typically see aircraft heat fuel for atomization and also to simply put more energy through the engine (more in, more out) as turbines will GENERALLY (this is very general I know) put out more and more power until material limits are reached (over temp/speed).
Fun fact, the SR-71 blackbird had a system to burn off the hottest fuel first, as it used the fuel on board as a heatsink integral to the airframe. It pulled heat away from the engines, avionics, etc.
Now in an automotive capacity typically you are fighting detonation. In this case cooler fuel can help combat cylinder temperatures and fight detonation. Understand that this IS hurting combustion efficiency somewhat but it's a lesser of 2 evils. Lose 2 hp on ideal combustion or gain 20 in a more aggressive tune?
There are other factors for specific vehicles as well. For instance, old porsche race cars had fuel lines routed over the exhaust and would experience vapor lock when fuel in the lines boiled. Fuel temperature management became essential, for reasons that had nothing to do with the actual running of the engine (well besides it NOT running
I'm willing to bet dollars to donuts these new cars with A/C mounted fuel coolers also have some kind of temp sensor for the gas and can adjust the ignition advance to make more power with a cooler gas temperature, without the worry of detonation.
*****TLDR: you, at home, will never notice a difference. Go make some ben franklin's and buy some expensive computers and maybe you too can realize the <1% power advantage of fuel heat management.