Epsom salts may help a little -- as the reponder says, they're soothing. I generally recommend cool,wet compresses, but a tepid bath is good too, and the salts can act as a very mild disinfectant (salt dessicates bacteria). Note that it's a burn, so the body responds by rushing blood to the surface to heal the wound. This can result in some degree of hypothermia, so one of your jobs is keeping the patient comfortable, especially as body temp is concerned. So don't let the bath get too cold or too warm. Note that, while it's rare, you can rush a badly sunburned patient into shock if you let them chill too far. If they feel uncomfortable, they are.
I'm not convinced about aloe or Aveena working, but I Am convinced that it's almost always harmless (barring very very rare allergies), and as doing no harm is the focus here -- aloe and Aveena are okay ( know there are studies on both sides, especially with aloe which may be as good as the claims say it is -- and they may be right). If it seems to sooth, that's good enough. Note that this isn't the case for worse burns, where you may be setting up an ER tech to have to scrub the stuff off, which is painful and potentially harmful. But for sunburn? Why not?
I might consider adding in an antihistimine like diphenhydramine, taken orally. Sometimes sun reactions include a histaminic reaction, which can itch like crazy, and this will fix it. Also, with 1st generation antihitimines like diphenhydramine, they make you sleepy, which will probably help the patient get a better sleep.
As to hot water? Wow -- I wouldn't personally consider it. A burn -- even a sunburn -- is an especially wide-area injury. The reason your body has a pain response to hot water is that, after a certain temp, hot water can damage flesh. Already damaged or burned skin is more susceptible.
As to holding it over an open flame or stove -- absolutely no -- forget it.
Lots of folk remedies are bantered about in a kitchen, and some of them are great (icing a wound fast may have started in the kitchen, for instance). But this one I can't see a scientific basis for and, until I do, I'll recommend against it -- with no offense intended to the contributor. I'll be pleased to address this further in Discussion if anyone wants.
The remarks about the blisters are right on.