I think it'd be really cool to add a histogram of particle speeds with an entropy counter. To control temperature, make particles gain a little momentum in a random direction when they hit the sides of the box.
Wouldn't they lose momentum to heating the environment?
At the level of particles, isn't "heating" the same as speeding up?
Yes! I was pointing out that particles typically lose energy to collision with the environment, not gain it (as the OP implied)
OP was suggesting a way to artificially control the temperature, so they would artificially add energy to raise temperature.
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.