The logic behind this is that when temperatures are cool, fuel is denser, so you get more fuel per litre pumped. Fuel is stored in underground tanks, where the temperature hardly fluctuates. So the fuel coming out of the nozzle is basically always at the same density, whenever you decide to pump.
The real money saver is driver behavior. Aggressive driving—rapid acceleration, high cruising speed, high braking speed—all those things are wasteful in three ways.
