The important thing for fusion isn't the average energy of the particles in your ensemble but the number of particles with energies around 15keV for D-D fusion.

The important thing for fusion isn't the average energy of the particles in your ensemble but the number of particles with energies around 15keV for D-D fusion. In the case of this experiment there was a potential of around that many volts around that palladium and if, theoretically, some deuterium could pick up a charge and cross that potential without running into anything else and then managed to run smack into another deuterium at the far end it had a high chance of fusing. There wasn't any a priori reason to think that those events would be common or uncommon and so barring experiment there wasn't any reason to dismiss cold fusion out of hand for temperature reasons. The lack of gamma rays was pretty significant evidence, though.