Firefox for a CPU these days isn't anything. IF you're at 45C at that which is basically idle; you may have a heat problem. Have you done any stress testing at all? I'm talking using Prime95 or similar?
Also, have you double checked with more than one software source for temperatures as some applications will differ to different boards. I'd do a little gaming or something a little more "aggressive" on the CPU and watch the temperatures in a couple different applications to make sure they are reporting right. If the load temperatures are getting over 65C then you may have an issue. When I shut off my fans on my 212+ I will idle/browse at about 32C compared to the 68-75F ambient temperatures in the room. If I crank them they drop the temperatures usually within 2C of ambient. So I would make sure the fan is spinning like it should and make sure that you're getting proper readings on temperatures.
If you do have a heat issue here's a couple things to check.
Thermal Interface Material (Bad thermal paste application?)
CPU voltage just too much for the 212?
Ambient case temperature not close to CPU reported temperature (which would relate to a poor airflow environment.)
How is your CPU fan set up? Does is completely shut off during idle? That could be an issue especially if you're running a fixed voltage system. The fans on my 212 can be shut down completely as I have them on a fan controller. If I do some media player with high res movies I can actually get the CPU to hit near 50C without a fan on the cooler running. So I'd check that to see if the CPU fan is set to some stupidly low settings.