Small, Inexpensive, Silent Gaming Is Here
Modern energy-efficient graphics cards make it possible to game on affordable, passively-cooled platforms (and they don't have to be massive, either). Even without the "just-in-case" fan we've been talking about, you shouldn't encounter any thermal issues.
As with any build, you'll want to balance host and graphics processing performance so that you don't create bottlenecks. If you're using integrated graphics, AMD’s A10-5700 is a good choice. If you have a passively-cooled add-in board, an inexpensive Ivy Bridge-based Pentium or Core i3 is the better option. They run cooler, and at $100 for a Pentium G2120, they aren’t really any more expensive.
The much-touted Dual Graphics feature that lets you match an APU up to a discrete card in CrossFire is pointless. Current-gen passively-cooled graphics cards offer better performance and efficiency, and they don't saddle you with the problems of multi-GPU setups.
It’s too bad that we weren't able to find any passively-cooled GeForce GTX 650s. Do-it-yourself is the only way to go if that's the direction you head. You'll want to decide for yourself if a third-party heat sink is worth the extra cost.