Yup, probably time to delid and change the thermal paste.
But before doing that, confirm that the temperatures really are what they are. If you have another AM2 CPU, try it out and see what that shows in terms of temperatures. The chances of the mobo misreporting are small, but still there.
Also, what software did you use for checking the temperatures? If just BIOS, then also try some different softwares to see what they all report. There's Speedfan for the oldschool, MSI Afterburner (doesn't always work for AM2 systems, IME), HWinfo, OCCT, AIDA64, and etc.
FWIW, 50C idle really is already too hot. If the CPU heatsink is the "normal" stock one with full-height and relatively dense fin count, your temps shouldn't be anywhere this high.
If this is of any help, the PC I'm posting from right now has a X2 6000+ Windsor with stock cooler. Under max load, it will reach around 60-65C, IIRC.
I'm not running it in stock mode, though. I have it underclocked to 2.4 GHz and running at 1.175V instead of the default 1.4V, which both greatly reduce the heat output, especially under load. I can do full clock (3 GHz) at 1.275V, which again also shave off about 10-12 Watts from the power consumption, which lowers the temperature by 3-4C under load. But I'm only doing that because my motherboard's VRM is starting to look crispy in a few spots (cheapo ECS OEM mobo for a Gateway PC.)
That said, how is your mobo's CPU fan profile configured? (Or is it even possible to configure it?) On my board, I can't do fan control and the CPU fan speed is a bit on the low side until things start cooking... so I have my CPU fan and rear exhaust fans swapped - that is, my rear exhaust fan is on top of the CPU heatsink (since it turns faster) and my CPU fan is doing rear exhaust duty. As a result, I have a system that can cope with really hot non air-conditioned rooms (configured this back in my college days so that this PC would be able to cope with the lack of A/C in the place I was renting.) In any case, you shouldn't need to turn to tactics like this. If the CPU has thermal compound going bad under the IHS, that should be resolved first before anything else.
FWIW, it's not just Brisbane, but most K8 and K10 CPUs that use thermal compound under the IHS. IIRC, only Phenom (I/II) and Athlon X4 don't, since these have higher TDP and would not have lasted with regular thermal compound under the IHS.