I already have a gaming desktop so the machine will only be used for media streaming, media playback, and youtube.
While an AMD APU looks attractive, I do have a hd 6770 laying around so I could get a cpu with graphics but I would like to reduce the heat in the case since its made out of wood and I'm already going to have tv tuner card and a sound card installed too (don't want to get an ATX board to save on space).
I highly recommend the Phenom II X4 960T. I just used it in a recent HTPC build of my own. The 95W TDP is great for keeping things cool and the Zosma (Thuban) memory controllers on the chip are more robust than the Deneb controllers found on other PII X4s so it's even more stable and better for overclocking if you're interested in doing so. I was lucky enough to get a chip that unlocked two extra cores, making it a 6-core CPU for the price of a quad-core. Overall, it's the best value at this price range.
I actually get most of my parts on eBay since the prices are even lower, especially for "older generation" tech.
The only CPUs without integrated graphics are the Phenom II and FX CPUs. I recommend avoiding the FX series since they pretty much have high power consumption. That leaves you with the Phenom II series.
Heat is directly correlated to power consumption. The higher the power consumption, the greater the heat generated. The following charts shows power consumption at different states for Intel's Sandy Bridge CPUs and AMD's FX and Phenom II series.
The Sandy Bridge CPUs consumes a little more power when idling (producing slightly more heat) compared to AMD's CPUs. However, once there is a load placed on the CPUs, the Sandy Bridge CPUs consumes less power than their AMD CPUs (and generates less heat).
The Ivy Bridge CPUs consumes less power than their Sandy Bridge counterparts (thus producing less heat). However,when OC'ed they do then to generate more heat than Sandy Bridge CPUs, but as long as they are not OC'ed this should not be the case. Unfortunately, only a single AMD FX-8150 is used as an AMD comparison.