You are essentially correct but that is just a part of the whole equation. It's an old machinist's trick. You heat a bolt and yes it expands faster than the surrounding metal so yes, initially it gets tighter. The bolt also cools faster; especially if you actively cool in with cutting oil or even water. Now it contracts faster than surrounding metal and momentarily becomes looser than it was.
That's for metal to metal contact but in the case of a bolt or screw that has any adhesive materil whether it's red or blue loctite, permatex, glue, whatever, heat makes these materials more pliable and at relatively low heat too.
In this guy's case, his waxing iron would be hot enough provided he could get it inside the binding to hold to the screw head.
I have done the hole heating before to loosen a bolt but have always done it by heating the outside area instead of the bolt. I have done it on bolts with and without loctite. Heating the bolt then trying to cool it faster does make sense when I think about it. I just never have done it that way or had to.