We have observed very rapid spontaneous heating of the cold solid methane moderator when irradiated by fast neutrons at low temperatures in the Intense Pulsed Neutron Source. In one instance enough heat was released to vaporize a fraction of the methane. We have also induced smaller rapid heat releases —both by slowly warming irradiated methane and by diminishing the effectiveness of cooling. An explanation for these observations is that energy stored in the form of reactive species (H, CH3,...) accumulates in solid methane irradiated at low temperatures, and is released by thermally activated diffusion and subsequent reaction. During irradiation, the density of reactive species can build up sufficiently to become unstable as the rate of heat release due to recombination exceeds the rate of heat loss to the cooled surroundings. Similar effects may occur in other cryogenic moderator materials, and may be responsible for the jets observed from cometary nuclei.