I never have understood how this mod works to give you better performance.

An engine runs and performs better, over the long run, at a higher temp. But just with anything in an automobile it is a balance, you want the engine to operate at peak efficiency, while at the same time you don't want it to get to the point of catastrophic meltdown. Research has proved that higher engine temps actually promote a more stable environment in the engine and the materials themselves. Also you don't want the temp to be so low that it inhibits the atomization of the fuel, which causes an incomplete burn, and in turn hurts performance. The transfer of heat from a metal to the surrounding air is not an instantaneous action, it takes time. The speed of the air entering your engine greatly diminishes the time for heat transfer. Air is also a mixture of many gases and each gas has different rates of expansion and heat absorption, so the transferring of heat to the intake air would be random and at varying degrees no matter what the temp of the engine is. The main contributing factor of high intake air temps is really the restrictive factory air intakes, forcing the air to soak in what is really an oven(the engine bay).
Now a turbocharger or supercharger is a different animal, as we all know the point of these is to cram as much air in as you can. So obviously the intake air is going to spend a lot more time in these heat soaked spaces than in the intake manifold its self. That is why when you do have these the air (in general) is cooled before it enters the intake rather than just before it enters the port in the head or the combustion chamber, which obviously would be tricky to do with a factory head that didn't have such things, and wouldn't really allow the time needed to truly cool the incoming air.
And by time I don't mean seconds, I mean microseconds, nanoseconds, and possibly even smaller increments of time.
Now I do understand why a lower temp thermostat would be essential in drag racing, running hot laps and such I see how lower engine temps could prevent a lot of blown engines. But for a street, road racing, or circle track engine I don't see how a lower engine temp would be vital or preferred.