I had an answer all ready that would have been the third post here, but apparently Max took the site down just as I hit Submit.

There have been lots of "answers" already, but in summary:

The rough rule is that 15 psi will raise the boiling point from 212F to around 235F (100C to 112C), but that's only an approximation.

Even with a good gasket, the lids sometimes hold stubbornly, but usually applying cycling of "on" and "off" torques repeatedly gets the things apart unless it's made it to "fully glued" condition.

If the prssure is equalized, the only thing likely to be holding it is that the rubber gasket between the pot and the lid is adhered to both pieces. That could be because the rubber has reacted chemically with the alumin(i)um and it's "corroded" on, or because the rubber itself has degraded to "gumminess," or some "gunk" that was in it when it was put away has wicked into the cracks and congealed/hardened.

New insert: Even if the gasket has hardened it will be compliant enought that the amount of expansion/contraction you can get by heating/freezing the Al isn't going to do anything helpful. (IMO) Serious heat (as with a blowtorch) will probably melt the Al before it degrades the gasket enough to be useful.

The only non-destructive suggestkion I can think of, other than "keep wiggling it," is get the inside of the pot - and the gasket in particular - "wet" again in the hope that the joint will loosen. I haven't had much success with lubricating from the outside (around the flange) but it might help(?) in a given case, depending on the condition of the gasket.

In addition to the "regulator" (vent) fitting, there should also be a "fusible plug" that can be unscrewed so that you could have two holes (in and out?) to circulate a liquid. If you can get only a small amount of liquid in, turning the whole thing upside down of course will get the liquid to the "top" where the gasket is.

Older gaskets often were of "natural rubber" but newer (within a decade or two) often are a silicone-based composition. Either kind, in my experience, tends to "harden" with age, although the later stuff is a little less prone to surface cracking. A mineral based solvent possibly would be more likely to produce breakdown of the gasket more quickly than soaps or animal/vegetable fats; but I don't really know what to suggest for a first try. Even clean water might help (especially if you can let it soak in for a while?).

The normal maximum operating pressure is typically 15 psi, and it's likely that anything much over about 20-25 psi may warp the lid enough to make it unreliable in re-use. Even 20 psi on a 10" lid is a little over 500 pounds on the flange that holds the lid down. Be careful with the pressurizing.

If you get the lid off, you'll almost certainly need a new gasket ($8 to $10 US the last time I bought one, but that's been 4 or 5 years ago). If you've pulled the fuse plug, it probably should be replaced (about $2.50 the last I saw). There are a couple of different constructions for the fusibles, some of which might be reusable, but others have a rather soft thread that may not seal if removed and replaced. A new small cooker (2 to 4 qt) may still be less than $40, although you'll have to check your local market. It may be simpler - and more economical - just to recycle the aluminium and get a replacement cooker.

In my area, there are two "Ace Hardware" stores that stock cookers, gaskets, fuse plugs and a few other accessories, but several others don't. The "big box" stores may sell new cookers, but almost certainly won't have replacement parts. New cookers should be easily found, if you decide to replace, but "canning size" are sort of expensive - on my income and with my inclination for using one. At least two makers still produced them the last time I looked.

(You might want to shake vigorously to see if it might be full of needles before taking it to the recycler, just to avoid "questions"?)

John