Far-seeker:
Since retrolefty did a good job covering the PWM aspect of your post, I'll dive into the theory a bit.Peltier junctions are devices based around the thermoelectric effect, specifically the Peltier effect, which describes how heat can effect the flow of current between two different materials. Like the Piezoelectric effect, the Peltier form of the Thermoelectric effect is a reversible process. Therefore not only can the temperature differential of a junction effect the current flow, the current flow can cause a difference in temperature between the two sides of the junction. With certain pairings of materials (e.g. dissimilarly doped semiconductors) this effect is strong enough to either cause a signficant temperature differential (i.e. heat one side of the junction, while cooling the other) if an electric current passes through it, or generate a small current at a specific voltage if a large enough temperature differential exisits accross the junction.
Does this help you understand this part a bit better?
Another way to think about it is this: in a fridge the coolant is pumped round and forced to evaporate (change state) in one place (absorbing heat), and condenses somewhere else (dumping heat). Think of the electrons as the cooling fluid, the change of state is when they are pushed from one material to another. Its basically a heat pump using electrons (or holes depending on the semiconductor). The change of state is more a change in entropy across a pn-junction I think.
Unlike mechanical heat-pumps the devices are low-efficiency (good mechanical heat-pumps / fridges push many times more heat energy around than are needed to power the pump - peltier devices use about as much power as the heat they move I think. One reason the devices aren't very efficient is that the semiconductors that exhibit the effect conduct heat rather well (short-circuiting the heat flow).
As soon as you power down a peltier the temperatures will thus equalize rapidly.