This being said, will using a dedicated card lower the heat on an APU? That is essentially what the Athlon 750K is, but I can get 40$ off of a motherboard through bundling locally if I go with the A10.
Could disabling 2 cores on the 6300 cut heat by NEAR 1/3 ?
What are you using it for? Gaming? If it's only light gaming / mostly a "work box" and you don't need that much GPU power, I'd suggest an Ivy Bridge i3-3240 or even a Pentium. It's "55w" is more like 45-50w in reality - and with undervolting you could get that down to nearer 35w fully loaded Prime. iGPU TDP included.
If you're gaming, then quite honestly, every CPU is going to be iGPU limited. And if you use a discrete GFX card (assuming you can fit one inside a 3.75" height case when many cards are 5" wide), performance-per-decibel ratio is often much higher with a compact Micro-ATX case with a 92mm heatsink / fan than a mini-ITX sized case with a "dwarf" heatsink. Tiny looks cool but is not so good when its noisier.