There are plenty of theories available to explain some or most cold fusion experimental results, but none of them has gained general approval among cold fusion researchers. The rudiments of a less-known but interesting theory have been proposed by Ron Maimon, who up until the end of 2012 was an active participant on physics.stackexchange.com. The theory goes well beyond my knowledge of nuclear physics, but I was able to get ahold of some details about it that make it more recognizable to a hobbyist like myself, which are mentioned in this Stack Exchange chat transcript. Prior to the chat with Ron I participated in an interesting discussion with Robin van Spaandonk, on the Vortex list, about some of the details of the theory as set out in the reply to the physics.SE question linked to above. Robin is knowledgeable about nuclear physics, and the discussion helped me to know what to ask later when I was talking to Ron.
The basic mechanism occurs when a K-shell electron is kicked out of its orbit around a heavy palladium atom in the metal lattice. That in turn creates a hole which can decay in various ways; normally it will decay either through an electron from another orbital filling the hole with a subsequent x-ray photon emission or, alternatively, through the ejection of an Auger electron. The energy involved in the decay of such a K-shell hole is on the order of 20 keV, an amount sufficient to cause two deuterium nuclei to fuse a significant portion of the time in a beam of deuterons.
Ron posits that when a deuteron is in the immediate vicinity of a palladium atom from which a K-shell electron has been ejected by action of an x-ray or a traveling alpha particle, the deuteron will preferentially receive the energy of the K-shell hole decay via electrostatic repulsion, thereby gaining 20 keV of energy. This makes the deuteron in a sense an "Auger deuteron." Should it fuse with another deuteron, the Q value of the reaction will be a very large 24 MeV, which will be shared with the daughter alpha particle and the spectator palladium atom. If I have understood Ron's account, there will be no gamma photon, as the reaction will have occurred close enough to the palladium atom for it to share in the momentum of the daughter alpha. The fusion cross section will be enhanced in the case where two energetic deuterons approach a palladium atom simultaneously; at the "classical turning point," i.e., the point at which the electrostatic repulsion of the positively charged palladium nucleus will start to push the approaching deuterons away, they will be in close enough to one another, as Ron alludes to and Robin clarifies, for their de Broglie waves to overlap enough to possibly result in a fusion.
Occasionally a fast daughter alpha particle will interact with a spectator palladium atom, causing it to gain or lose some number of nucleons and resulting in a transmutation to another element. This is understood to be a side channel and not the main source of heat. The reaction is sustained as a result of the energetic daughter alpha racing through the lattice, ionizing palladium atoms as it travels, triggering in turn the mechanism described above. According to this theory, the things to look for during and after anomalous heat are x-rays, helium and transmutations certain numbers above and below the mass of palladium.
An issue that Robin had with Ron's theory is that he thought that the ionization caused by the traveling alpha particles would be too inefficient to result in enough K-shell holes. But he also pointed out that, if something like this were happening, you might see a similar effect in the nickel/hydrogen system. In that case it would be the fraction of deuterium in light water interacting with energetic protons, rather than p+p fusion, that would be taking place. If I have understood Robin, an attractive detail of Ron's Pd/D-focused theory is that it potentially provides a way to keep the energy needed for D-D fusion around long enough to sustain a continuous reaction.