The quest for the hot stamper or is it a myth

Caveat Emptor. 

Can someone define "hot stamper" and explain how to identify/determine whether you have one, the differences between versions, and why anyone should care? What makes a "hot stamper" different from other pressings of the same LP?

Sorry but I see this term thrown around here and there but don't really understand what all the fuss is all about.

Its not a myth. Its a misnomer. Or whatever the word is for a term being misused. The stamper must always be hot. Vinyl simply will not flow properly with a cold stamper.

As for the rest, if you really want to understand then I suggest you spend an afternoon tracking down and reviewing MF videos. Those little codes scratched into the vinyl on the inside close to the label? They identify which stamper was used. So you can tell just by looking if your LP came from the original or one of the later copies. 

Sorry I don't have a link, but you could do worse than spend an hour listening to Mikey.

There have been many threads, here and elsewhere, on Better Records and Tom Port. I have never bought a record from him (for reasons explained below), but do agree that the latest audiophile remaster of a well-worn warhorse may not sound better than an earlier standard issue pressing. The problem is, it’s case by case and there are few rules of thumb to ascertain this based on data, short of listening to the records in question.
My experience is that first pressings aren’t always the best sounding, that factors like mastering engineer and record pressing plant can affect the sonic outcome, sometimes to a considerable degree (things you usually can ascertain from the deadwax), but there are always exceptions. And buying old, used records invariably involves issues of condition. Grading is a haphazard enterprise at best.
I’m not against spending money on a record, but I already have most of the "better" pressings of mainstream rock/pop/soul records that I care about, sometimes, multiple copies. So, buying more of those is of little interest to me at this point.
I suppose if you didn’t have the time and energy to buy 1/2 dozen or more copies of a common record and compare them yourself, and had a deep pocket book, Tom may be the way to go if those are records you need to fill in, or start, a collection.
There are copy to copy differences, to be sure, even among records that are otherwise identical, but that way lies madness. I find the best representation I can, often by buying multiple copies and comparing them myself. That means I have a lot of duplicates of some records, but in many cases, the difference between two different pressings may be one of emphasis, rather than one that is an absolute "best."
I do think the term ’hot stamper’ or ’white hot stamper’ is marketing speak from Tom Port and does not reflect anything other than his (or his staff’s) determination that a particular copy, based on their sampling and comparisons, sounds demonstrably better than another. Anecdotal reports from people who have made meaningful comparisons on Hoffman is instructive, at least in older threads where there were thoughtful, detailed comparisons, rather than conclusory declarations about a single "best" sounding copy. And, of course, on some records, there is a general consensus of ’known’ good sounding copies based on deadwax, pressing plant and mastering engineer. The best way to ascertain this, in my estimation, is to do the comparisons yourself if you have time. Sometimes, early pressings are now so valuable that the objective is to find a good sounding less expensive copy and that can be an interesting process as well.
Some of it is about trade-offs, rather than absolutes. And, there are times when the audiophile reissue does sound better than an "original" pressing (whatever that means based on country of origin, mastering engineer and plant). I will share records among a few friends sometimes for these comparisons so I’m not out of pocket all the time.