You could try resetting the SMC, but it sounds like you may have a defective battery. Here is the link:
http://www.apple.com/support/macbook_macbookpro/batteryupdate/
Be sure and print out the article and take it with you, as not all Apple employees are familiar with this particular battery program. But if your battery meets the criteria, you should be able to get a free replacement.
However, it sounds like you may have developed a heat problem, and this may well be contributing to your battery problems. There are a couple of things to check:
First, run the Apple Hardware Test and see if you get any error codes that might indicate a failing thermal sensor (SNS) or fan (MOT). Use iStatPro to check that both fans are running and that they speed up with the heat and that both run at about the same speed.
Second, open Activity Monitor and set it to show all processes and look for some process which is using a lot of the CPU. Sometimes these things will run in the background and cause excessive CPU usage and heat.
Good luck!