How much heat.... How long is a piece of string? Experiment carefully using an empty key cup heat it just enough to get the glue moving (e.g. high D). Shouldn't be runny, more treacly. When it gets runny, pads drop out. Takes a bit longer on the sax with a pad in it. If you overheat shellac it boils quickly and lifts throws the pad out. If you don't overheat, you won't damage the lacquer.
Can use a spirit lamp, low power gas torch, but don't use something that has a yellow/sooty flame. Some guys use a modified soldering iron, but I'l let JBTsax describe that. Not sure about the heat gun - they will be hot enough but tend to heat everything. I've heard people say they use them.
You'll need to heat the key in place on the sax to adjust the pads. By having a static lamp/torch with the flame going up you can hold the sax over it in such a way that the heat mostly only gets to the key you're working on. It's harder with a fixed sax and moving lamp as the flame goes out in an upwads arc. Keep the sax moving, don't let the heat build up in one place - and give it time to get through the glue.
If you're working on an unlacquered silver sax, make sure the flame has as little air as possible without going yellow. This minimises the oxidation of the silver. And in any case work with a minimum of heat. Too little does no damage and you can easily add more.
Be really careful of burning corks/plastic parts/pearls.... And remove any pearls near to the heat (low D/E). Best to shield any you don't remove with aluminium foil wrapped loosely around, but not so loosely that you leave a path for the flame to get in.
If you make sure the tonehole and key are flat/straight to start with (dry fit the pad without glue and test on the sax), you should only need minor adjustment once fitted. Pay close attention to how high the pad sits in the cup and make sure you maintain this when you fit with glue.... With smaller pads you may be able to put the pad in the cup slightly high, fit to the sax, warm and get it to self adjust with gentle closing pressure, but this is harder with the bigger keys. Not sure why, could be me....
Low D is a bit tricky to regulate. Make sure you really understand the linkage before touching it, including the linkage to bis Bb and G#, not just E and F.