Is it possible to limit resources to a game? Or forcibly limit the FPS
Let's look at the two things you suggested, as these are two separate approaches to solving the issue.


Limit the resources provided (presumably by limiting the CPU.)
Cap the framerate


Limiting the resources provided is pretty easy (provided you're willing to work with a little bit of third-party software.) You can use cputhrottle to limit the usage at the system level (better explained here.)

Capping the framerate is generally done at the level of the game. Unfortunately, to my knowledge, there's no way to set your framerate cap either lower or higher right now.  So you're stuck with throttling the CPU, although given what you're trying to do, that seems like a fine option.