I remember well the phenomenon of "cold fusion" as it was dubbed. This was back in 1989 when Professors Stanley Pons and Martin Fleischman claimed that they could extract 40% more energy in the form of heat than they had put in the form of electricity into an electrochemical cell containing deuterium oxide ("heavy water"). They proposed the deuterium nuclei had undergone a nuclear fusion. The potential implications of this were staggering: that rather that trying to mimic the massively high temperature conditions in a star such as the Sun, of some hundred million degrees or so as are necessary to overcome the strong Coulombic forces that tend to keep two positively charged nuclei apart, as in "hot" plasma-fusion, it was feasible to somehow overcome this barrier such that the process could occur at room temperature.
Pons and Fleischman became largely dismissed as charlatans when many other research groups around the world found themselves unable to reproduce their results and confirm their claims, which were accordingly dismissed as unfounded. However, note the comment below to the effect that the phenomenon has since been confirmed in many highly credible laboratories around the world. I remember there were some really quite bizarre effects found by other workers - for example, one young man was killed when a cold-fusion cell exploded while he was trying to demonstrate the phenomenon of "fusion in a test-tube" as the popular press described it. So, something real was happening, fusion or not. A senior scientist and champion of cold-fusion, Dr Eugene Mallove, was murdered during the furore, which incited a number of conspiracy theories at the time.
The matter never entirely went away and I recall reading an article either in The Guardian or New Scientist (or both) to the effect that a scientist in the US had claimed to have demonstrated fusion when he exposed hexadeuteroacetone (that's C3D6O as opposed to the more common C3H6O) to ultrasound. He was crucified by the scientific community, as I recall, who had decided that cold fusion did not exist, and when they do that, God help you, if you claim otherwise - you will be castigated as a heretic, with all the ardour of the Spanish Inquisition. The most fervent believers, both scientific and religious, tend to bang the drum of their dogmas with equivalent enthusiasm; trampling the opposition where they may find them.
However, a professor in Japan has apparently demonstrated that if deuterium gas is passed into a reactor containing composite palladium-zirconium oxide (Pd-ZrO2) nanoparticles, Helium-4 is produced (a sure sign of fusion?), the temperature of the reactor rises and its centre remains warm for 50 hours.
If this is true it is absolutely fascinating and perhaps the accepted laws of chemistry and physics will need to be substantially modified, as has been said. However, from a practical point of view, that of dealing with the energy crunch, is the result of any importance even if cold fusion is a reality? I don't think so, frankly. I have not seen any figures for how much Pd and deuterium gas are used to run this cell and how much excess heat is produced. However, I have yet to be convinced that the energy needed to produce deuterium gas (by the electrolysis of deuterium oxide - "heavy water") and to make enough heavy water in the first place to feed the electrolysis units, will be offset by the final thermal output of the "fusion" reactors.
Then there is the matter of availability of palladium metal, the energy for its fabrication into the composite nanoparticles and so on, and how would the heat energy be extracted usefully, say to heat buildings or drive electricity turbines? The problem of energy extraction is even worse for "hot" fusion, from a plasma that even if it can be sustained, would produce ultra-high energy neutrons that no known materials are yet able to withstand, from which to extract thermal energy.
Very interesting indeed if it's all correct, but so what? We need more pragmatic solutions than fusion, hot or cold, to preserve lifestyles as we know them as we begin to see the depletion of conventional fuels.