Sounds like a simple case of the unit overheating. I'll take a guess that the video was using flash, like from youtube or something similar. If true, then it would all but confirm it. Flash for the Mac is just plain horrible. On one of my Windows boxes, with nearly identical specs to my Mid-2010 iMac, I could go watch say a couple Red vs Blue episodes with no problem. I do the same thing on my iMac, and probably by the end of the first video I hear the fan ramping up. If I let the system sit for a minute or so after the video stops, the fan cycles down.
So basically Adobe has done a real bang up job with Flash for the Mac where there doesn't appear to be any GPU acceleration going on, and more than that, it just seems far less efficient than the Windows version in general. Whether that's because DirectX is a far more comprehensive solution than Quartz and OpenGL I can't say, but Flash for the Mac will really put some strain on the cooling systems of a Mac; even a Core i7 Mid-2010 iMac. So given the 13" MBP only has the one fan to cool the entire system, I'd just try and limit the amount of online videos you watch. There's really not much else you can do. Taking a can of compressed air to the fan may help a little, but will really only do so much.