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When PUFA is present and oxidation is going on, you're tending to be torn up with free radical lipid peroxidation and such. So the PUFA does feed oxidation and can help with weight loss, but that turns out to be almost purely destructive. You don't want to lose weight that way. The excess of thyroid, when you have a moderate excess of thyroid and DHEA, which increase the wasteful use of oxygen, that waste is protective. Animals which are uncoupled, and especially those which have a low PUFA in their tissues, are longer lived.
The saturation index, if an animal's fats are highly saturated, it has a longer life. And that means that it can run its oxidative metabolism at a much higher rate being uncoupled and living longer because its fats aren't set to explode or catch fire with the free radical activity going on.