The basic ideas... heating to 1500 or so puts the carbon atoms into solution relative to the iron atoms within the steel. Quickly cooling the steel in oil sets the atoms into place into a structure called "martensite", which is hard but brittle. Tempering reduces the brittleness. Two temper cycles are recommended to make sure that all the atoms are nice and relaxed
Tempering temperatures are usually in the 350-500 range.
And for FIF, they show the quench because it's exciting. They leave out the tempering b/c it's boring watching a blade sit in an oven. For FIF, the blades are tempered overnight by Jay or Ben.