Does that mean hydrogen would be used up much more quickly in high temperature stars? If I remember correctly, that's why large stars have shorter lifespans.
Using some hand-wavy arguments you could say that fusion pauses a star's collapse, so the more massive a star is, the more energy generation it needs to stay in equilibrium during this pause.
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.
The solar sunspot cycle is caused by the periodic inversion of the polarity of the sun's magnetic field.