Here, according to Mike, we had a model 37 pump resting on the owners lap when a shell in the magazine tube discharged. Mike gives us a bit of a clue when he says this happened a long long time ago. All of the forensic evidence is long gone, so about all we have is conjecture and old memories as clues.
I had thought about a "cook off" scenario, but realized that usually happens after extended full-auto fire when the barrel and chamber get extremely hot. Even in the hot Alabama sun, it isn't likely that you'd get a pump shotgun that hot... particularly in the magazine tube. Too bad we can't see the shell casing to examine if there was any damage to the primer. It's doubtful if the powder spontaneously detonated, but the old primer could be a different story.
It wasn't until after 1935-1938 that true non-corrosive non-mercuric (NCNM) lead styphnate priming compound mixtures became pretty much the standard because it was much more stable and much less corrosive than the potassium chlorate and mercury fulminate compounds that had been used previously in primers or percussion caps. Mercury fulminate, in particular, had a nasty characteristic of being so unstable, that it would spontaneously explode for no apparent reason. Since primer manufacturers were hard at work experimenting with different compounds that addressed the problems of instability and corrosion, it is entirely possible that the shell which detonated in the magazine of Mike's friend's M 37 had an old primer that was composed of a mixture that was unstable enough to just explode in a magazine tube on a sunny day. Mike's description of how the wad and shot remained inside the magazine tube sounded like what happened when I got the brilliant idea to put some of my Dad's shotshells into holes poked in a cardboard box, and shot at the primers with my pellet rifle. The shells would go flying, but the heavier shot charge simply dumped into the box. Stuff like this is why so many teenage boys never make it to adulthood.
Anyone who has spent enough time in an organic chemistry lab can tell you just how sensitive and unstable some compounds can become under the right circumstances. In college organic chemistry, my classmates and I played around with nitrating just about anything we thought might explode. Once, I made some nitrocellulose, or gun cotton, and took it outside to dry on a rock in the sun. When I came back later to get it, all that was left was a scorched mark where it had rapidly burned. We also played around making ammonium triiodide and nitrogen triiodide, which are highly sensitive contact explosives that would probably get you in trouble with Dept. of Homeland Security today. The ammonium triiodide was fairly stable as long as you kept it wetted with acetone. A friend had some in a small vial in his apartment, and the stopper apparently was loose allowing it to dry out. Someone slammed a door in the neighboring apartment, and it blew up causing minor damage. I had a couple minor explosions in the lab just distilling organic compounds in a reflux condensor, and allowing them to boil dry in the flask. We started making a batch of nitroglycerin, a very simple process, but thankfully lost our nerve. Coincidentally I think, some of these misguided experiments came when we would have cocktail hour with ginger ale and anhydrous 200 proof ethanol when the professor left for lunch.