Personally id say that to claim "How stars work has nothing to do with how this method works, which is the issue." is retarded considering that is exactly what they point out in the episode.How stars work has nothing to do with how this method works, which is the issue. You do realise you're speaking in absolute terms about what is by definition unknown pseudoscientific nonsense, right? The stages in the life of a (regular) star are predictable, in accordance with its mass, composition and nuclear fusion. That progression cannot be somehow changed, and certainly not by the simplistic "make star's core temperature hotter", which is the exact opposite of what any sane person wants to do to a star to make it more suitable to sustaining life.
The other comments are in regard to the star being a MASSIVE red giant but in fact it could very well be a red dwarf, as the proportion of hydrogen in a red dwarf is consumed, the rate of fusion declines and the core starts to contract, the gravitational energy generated by this size reduction is converted into heat, which is carried throughout the star mostly by convection rather than mostly by radiation like other stars do.
In fact in a later part just before the scientist slips Troi's mum a length he directly mentions deep convection patterns and that he thought he had accounted for them and other things while musing over the faliure.