You don't mention a history of when this started. If you haven't done a software upgrade for awhile and it started doing it all of a sudden, then maybe it should be something to investigate further. If you've done OS, browser and/or Flash updates recently, that may part of the problem.
If the websites you're visiting contain videos (you may not be looking for videos but it may have video ads), then the issue may be that the 2007 doesn't support hardware video decoding for certain codecs that are popular today - H.264, for example. That, combined with the fact that a 2007 processor is pretty old technology, then I don't think that it's unreasonable for the processor to be working at full-tilt. It used to be "only browsing the net" was not that taxing for a computer. However, that's no longer the case. It used to be that just about the only times I used to hear the fan on my 2012 Mini quad-core was when I ran Handbrake. But now I find that when I visit certain websites at certain times, the fan may start running (not full-tilt, but audible). (I disable hardware acceleration in Firefox, so that may be part of my issue.) If this high-temperature occurs in the plainest of web pages (the Google home page, for example), you may have a problem but seeing that the temperature is fine until you start browsing, I think it's just that you're visiting sites that require a lot of processing power.
One thing you can do - open up the computer and see if there's a dust buildup. If there is, be careful how you clean it - you just have to remove the buildup - it doesn't have to be spotless.
