Start it playing a replay then pause it.
It's the physics engine that causes the CPU hit, even when the game's idle in SP/MP it'll still hammer your processor. When it's paused on a replay it'll halt the physics calculations.
To a lesser degree the same applies to ghosts. Turn them off to free some cycles if you must leave a game running rather than a paused replay.
As for other ways of freeing muscle, minimize the game to save your GPU having to render it, but make sure you have graphic reloading turned on in options or you'll get weird glitches when you pop it back up. It'll cause the game to freeze for a second or two while it flushes and reloads everything into VRAM, but for what you're aiming for it shouldn't be an issue.