The chemistry of those handwarmers is pretty simple, just iron filings allowed to slowly oxidize when in contact with air, releasing heat, an "exothermic" reaction. But the speed of oxidation is affected by several factors. One is the concentration of oxygen. As Paws discovered, if the packets are trapped where air cannot diffuse in, they shut down pretty quickly. Salt is added to the mix, to promote mechanical breakdown of the thin layer of iron oxide so the underlying unreacted iron can combine with more oxygen. The action of the salt is enhanced if it gets a little moist, which can accelerate the process, to the extent that the packet might injure skin by blistering. A lot of moisture, such as happens if the packet gets sopping wet, for example, can isolate the iron from air and its oxygen, shutting down the oxidation.
An aside: a more complex process occurs when shredded iron and shredded rubber get wet, and oxygen infiltrates this mixture, resulting in further breakdown of the rubber into a slimy hydrocarbon mixture akin to crude oil, simultaneous with the generation of heat, lots of it. Sometimes enough to get that slime itself smoldering. Old shredded steel belted radial tires have been used as fill for slide areas, one of them across the Columbia near Ilwaco, inside Cape Disappointment State Park, leading to the catastrophic breakdown described above. Hydrocarbon slime leaked into the Columbia, prompting the removal and replacement of the shredded tire fill with inert gravel and rock, to the tune of several million dollars.
Old steel-containing tires have been know to do this, if in sufficient mass, at bootleg dumps, various places around the globe.