I have been using Chrome on my laptop and haven't noticed any severe battery drain. With chrome open, my laptop manages to work for ~4 - 5h from battery which is normal. As for memory management, yeah, it could be better.
I was running a 212 that was left from a previous build with my FX8320 and I could overclock it to 4GHz with no problems. I think that 212 will be much better than what you have right now and it will cool your cpu at stock pretty well.