If that is how long your battery last, I would say yours is about gone.  If you want to use your computer on battery power, then by all means get a new battery.  However, I don't think that is the cause of your computer getting hot.  My guess would be your computer is dirty on the inside, which causes it to trap heat inside.  It could also be that your computer is running more programs in the background than it was before.  So you might try cleaning the dirt out with compressed air from a can, not your air compressor.  Just blow out all the air inlets and exhaust that you can find.  If it is still running warm, you might need to reload the operating system or at best clean your hard drive up.  Also, as your computer ages the thermal grease on the heat sinks tends to dry out and they don't dissipate the heat as well, so it could just be an age thing.