For any given story purpose, some variant of nuclear energy will get you what you want. A society which has all the electricity it wants? France, with the volume dialed up on their nuclear program. A powersource that keeps the buried vault running for thousands of years? C-14 diamonds will generate a tickle of current for more thousands of years than any vault is likely to last, and if you somehow have a few tonnes of them, it is no longer so much a tickle, and more of a small river.
IMO the best way to go about it is "this black box / space rock / whatever generates infinite heat, deal with it and don't ask how it works". Science-fiction is allowed this kind of handwave, but trying to explain it with half-baked science is liable to provoke eye-rolls among the readers.
If it's preferable to keep it real, nuclear energy is indeed the next best thing.
Worldbuilding is fun, writing is a chore
It still violates the law of conservation of energy, because emotions are not physical objects. They are the results created by chemical reactions that occur when in contact to stimuli, programmed by our genes. That would not be the emotions fueling the psychic powers, its controlling them.