Temperature doesn't affect pressure, it affects density. Cool are is more dense than warm air.
The analogy of tires and balloons is flawed because the amount of air in the space hasn't changed, only the density. Now, with the reduced density, there is less volume, and less volume in a given space equals less pressure against the inside of the container it's in. This is why newer cars have nitrogen in the tires, it's less affected by temp changes and so the density isn't as affected and tires maintain a more equal pressure with changes in weather.
With engines, if it's normally aspirated, we tend to do things to try and keep the air cool to get a more dense intake charge. Hood scoops, cold air boxes, air gap intakes etc.
The other ways to increase the "density" is to use mechanical means, blowers, turbos, or chemical means, nitrous oxide etc.
The "cooling" of the heads is not going to matter since you're not "cooling" a flame. The burn is the burn and whatever made it into the chamber, is there to stay, until the valves open and let it out.
Science.... :)