My 2010 MBP's battery wasn't holding much of a charge anymore. The left fan also wasn't working.
The fan and battery were super easy to replace with iFixit's guides. My laptop is now being cooled properly and the battery is lasting just as long as it did when I first got my MBP. The only difficult part was getting the battery plugged in properly.
Be sure to get the battery connector pushed fully into its socket! This task was quite challenging for me and took about 10 minutes worth of carefully positioning and applying appropriate pressure. It appears that this version of the battery (non-Apple) is more sensitive about how it's positioned than the original battery.