Nah, the goal isn't to add or subtract energy, just change the entropy. If you have a process that on average doesn't change energy, but makes the distribution

Nah, the goal isn't to add or subtract energy, just change the entropy. If you have a process that on average doesn't change energy, but makes the distribution of speeds more or less narrow, then that is temperature control. I thought adding a fixed amount of momentum in a random direction (where higher temperature = more momentum) would be a way to control temperature. However, that actually increases energy on average, so you would need some way to lose energy to the environment as @ijustlovemath pointed out.