macbook suddenly powering down

I have a macbook I bought in 2009. Recently it has started suddenly turning off when I have it unplugged on my lap. The battery is fine- it's at about 60% when it "crashes." It hasn't happened at all when I have it plugged in on my desk, so I'm wondering if it's overheating when its on my lap. But if so, then why is this a new problem? It used to work just fine on my lap. The computer simply turns off instantly and with no warning. I plug it in, set it down on my desk, and push the power button, and it starts right back up just fine, but a little slowly. Should I take it in to an apple store to get the hardware checked out? Or just buy a cooling pad and see if that stops the problem?