The theory of cold fusion is that when hydrogen is adsorbed into palladium metal the hydrogen atoms get mixed with the electron "gas" in the metal so that the protons are able to pack close together so that meson tunnelling occurred. This makes a proton-proton atom (it is at a lower energy level than two separated protons) which then emits a positron to form deuterium which sits at a lower energy level level than the two hydrogen nuclei it came from.
The deuterons fuse in a similar way to form helium at a lower energy again.
The positrons emitted combine with electrons emitting two gamma photons at the annihilation frequency the recoil of the nuclei formed make the reaction hot and some gamma photons escape.
If you put hydrogen in a tube with palladium filament suspended inside after a few days the filament glows red hot and after a while goes white hot and makes a very good lamp.
If I recall, I did this experiment at a government lab, somewhere in England in about 1969. I was severely punished for my invention and put on routine test work.
They said my invention was "strategic" and I should say nothing for thirty years.