The other answers describe the "materials science" mechanisms of iron vs. temperature. I'm going to add this:
Matter "tries" to reach a minimum energy state whenever possible. In general, then, if you cool something as slowly as possible, you'll come closest to a solid which is a perfect crystalline structure. See "annealing."...
You are mixing apples and oranges. Many steels harden by rapid cooling, but very few other metals do that; specifically, only aluminum bronze and certain titanium alloys. Many metals will strengthen by age hardening; Rapid cool softens, and then time at a lower temperature strengthens them.
There are a myriad of combinations, like HSS (high-speed steels). ...
The effects of heating-quenching a metal is explained below
Transformation hardening is the heat-quench-tempering heat treatment cycle addressed earlier in this article. It's used to adjust strength and ductility to meet specific application requirements. There are three steps to transformation hardening:
Cause the steel to become completely austenitic by ...
In short the heat treatments in steel change the phase of iron between the following phases:
(Actually quenching does not allow low temperature phase changes to occur, so effectively the phases are sort of "frozen" in their high temperature equivalents).
Figure 1 : example of continuoous ...