[mnw21cam]

There's a negative feedback loop there. That is, a star of a certain mass needs a certain amount of energy production in order to keep it from collapsing, and that amount of energy production is automatically achieved, because if it were too low then the star would collapse a bit, and increase it.

Therefore, the rate of energy production isn't a consequence of the temperature. The rate of energy production is regulated, so effectively the temperature is a consequence of the required energy production instead.

[xattt]

Would this be one hypothesis for the solar sunspot cycle?

[bananabreakfast]

No, the balance of gravity to outward radiation pressure from the core is static in nearly all stars that aren't some of the largest we have observed.

The solar sunspot cycle is caused by the periodic inversion of the polarity of the sun's magnetic field.