Battery replacement related to Loud fan?

Alright, so I'm a bit of a novice when it comes to the inner workings of my macbook pro but this is what's happening.

I bought my machine about 4 years ago, i have 68gb free, I am a student and usually running firefox, a word application, and the vlc media player.

About 2 months ago, my computer started to get really hot from playing a videogame on it. This game would really drain my battery fast because it was heavy duty. My battery has needed replacement for awhile (says so in the battery info) and now the battery lasts maybe and hour and a half. I checked my fan a month ago, cleaned it out entirely and the noise still persists.

What I am wondering is, since my battery life is poor, the battery dies quickly. Is this what is making my computer hot and thus making my fan drone CONSTANTLY and making my computer so loud?

I'll buy a new battery, that's not a big issue but I want to at least have an idea if that will solve my noise problem.

thanks