When paused on a non-active (background) desktop in OS X or as a fullscreen application in the background (not the Minecraft settings fullscreen; the OS fullscreen), the app's CPU skyrockets to more than double its normal pause level and my computer starts to rapidly heat up.

To replicate:
Launch Minecraft and open up any world.
Hit OS X's green fullscreen icon.
Pause the game and switch back to your normal desktop, leaving the game fullscreen.
The CPU will rapidly increase and after several seconds your computer's fan should start to ramp up. The energy usage will also soar.

Once you switch back to the fullscreen Minecraft, the CPU will drop back down.