But we know that it does. The sun is not a thermonuclear furnace. Stars are plasma physics phenomena and behave like lightning rods as focus points for cosmic discharge. As they travel through regions of space with greater or lesser electrical potential difference from themselves, they heat up and cool off.
www.thunderbolts.info
Your paradigm problem is false.
Human nuclear furnaces have control rods and fancy gear to make damn sure they don't heat up or cool off randomly.
And our solid fuel nuclear plants aren't bubbling pools of hot gas with random mixing of fuels going on.
There's no reason to think that a natural thermonuclear reaction in a huge hot bubbling bubble of gas wouldn't heat up and cool off a bit from time to time.