Older bios had trouble reading temps. If there is a new bios available, see if it fixes temp readings. I dont suggest you flash the bios though, unless it fixes a bigger problem. Just knowing that it reads 10c high is good enough.
I recently messed up a stock installation of an Athlon64 x2 HSF. I had aligned the HSF to some components on the motherboard but realized after planting it down that part of the CPU heatspreader wasn't even covered. I took off the HSF (had to pull slightly to unstick the thermal paste, part of which transferred to the CPU spreader) and then aligned it properly and planted it down again, this time fitting the screws in.
Under Core Temp, idle temperatures of both cores looked fine and within 1-2C of each other. During load, one core would reach 58 while the other remained at 53. Suspicious, I took the case apart and reinstalled the HSF, this time cleaning both surfaces and putting on AS5 (which looked the same to me as the stock paste - opaque gray and highly viscous). Afterward, Core Temp reported 48-50C for both cores under load.
Based on this, I've come to think that in cases where the cores don't reach the same temperature under load, there's likely a problem with the HSF installation. Perhaps there was too much paste on one side... or perhaps the screws on one side are looser than on the other. This probably won't break a stock processor, but I'd think it would significantly affect one's overclocking success.
Thanks for the insight into your CPU HSF experience.
I didn't think that both cores should be equal at first anyway, since I thought one does the hardwork and the other does sod all. So it now looks like they both try and share the workload as equal as possible, thus should be giving a similar temperature reading on both cores under load.
I'd say roughly I get a 5C variation between the cores all of the time. Though this has been on occasion even 10C more when loading a program.