Theories of bolt heating (I) Besides the common way of loosening a bolt by heating its nut (or whatever else it's screwed into), there are some interesting theories of how heating the bolt itself helps, at least sometimes. One such theory is that heating and the cooling a bolt loosens "corrosive bonds". It's been said that this is not really a chemical process. So, how does heating and then cooling two rusty surfaces reduce the coefficient of friction between them? (If that even works, that is. I haven't seen an experiment that was isolated this proposed mechanism enough; pointing out more empirical evidence for/against this would also be appreciated.)
 A: If you heat and cool things you induce thermal stresses inside them.  If the object is made of two other objects bonded to each other this can cause the bonds to fail.  In the case of a rusted nut & bolt, the bond is the rust & other crud which is preventing you undoing it: the bond is usually much weaker than the steel components it is bonding. Rust will also have a different coefficient of expansion with temperature than steel, further increasing the stresses around the bond.  Finally, rust is much more brittle than steel, so it will fail well before the steel does.
So, in summary, the general trick is to cause all sorts of stresses inside the bolt & whatever it is screwed into, and hope that the bond between them fails before they do: it usually does.
The problem with doing this, of course, is that you often have to get quite a lot of metal quite hot, which can be hard and may not be good for paint &c.

If there is an engineering SE this might well want to be in it: it kind of is a physics question but I suspect a lot of physicists would not regard it as such.
A: If you heat the bolt, the heat will also be transferred to the nut. But the interface of the parts is a thread, and partly corrosion products, which are typically porous.
So the heat transfer will be much slower at that interface - causing the nut to heat much slower. 
The bolt expands before the nut expands, causing mechanical stress and some movement in the thread.
It may even force the nut to expand plastically.
When the nut has heated up too, you cool the bolt and make it contract
before the nut contracts, causing more mechanical stress, and reducing the
pressure at the interface, which is where it's stuck.
When the bolt is cooled, but before the nut has cooled too should be the best moment to apply torque to loosen the bolt.
A: The result of heating the nut is  the expansion of the gap between the bolt and the metal edge of the hole and thus the reduce of the friction force between the two surfaces.
You can find some excellent answers here:
Will a hole cut into a metal disk expand or shrink when the disc is heated?
