Athlon 7850BE

http://www.cpuid.com/download/hwmonitor/HWMonitor_114.z...
use that, tell me what cpu temp and core temps are

I am using that as well. The CPU temp is 51-52C idle and gets to 61-63C max while running 3dMark Vantage two or three times in a row. The Core temps are 32-33 idle and get maxed at 41-43C under 3dMark Vantage tests.

well i run a 7750BE. i got a little bit of an overclock on it (3.1ghz 1.35V). When i let coretemp and prime95 run for a few hours i usually end up with a high core temp in the mid 50's, depending on the air temp. So far it hasn't given up the ghost.
Anyway AMD lists the max temp at 73C for it, most people say 10C below is best for a max, and 15 for a 24/7. so unless you run prime95 24/7 you should be just fine. Even using your higher cpu temp.
If you are concerend get a new HSF, the one that came with my 7750 was total garbage, you probally got a simmilar one, a tiny little thing with a 60mm fan. A $10 one would most likey preform worlds better. (I use an old alpine 7 i had laying around)
The BE's were aimed at the overclockers so i think they just put any garbage HSF in there they had assuming 99% of the people that bought it would put it right in the trash.

ref for 7850 specks.
http://products.amd.com/en-us/DesktopCPUDetail.aspx?id=...

Me three  ,,I am running mine [7850be] with an Arctic Cooler 64Pro,and the temps never get over 40+c as far as I know,the thing that I like about the A Cooler64 is that it removes air all around the ram,northbridge and cpu area,which in a large server case is really handy.. 

So should I be concerned more with the CPU temp reading or the actual Core 1 and 2 temp readings?

usually the core temp is higher than the cpu temp, so cant say 4 sure, but once u stay under70, dont stress, try not to oc

That's the thing. Right now, my CPU temp reading is 52C, while both Core temps are 33C each. I don't know which one to pay more attention to when looking at the readings.

I have the same problem as you. NO ONE ON THE PLANET KNOWS THE ANSWER!!!!!

I've got a 7750BE, I run it at 3.0Ghz and it gets around 60C under load, I wouldn't worry about your temp, it's not hot enough to damage the processor. Oddly enough my core temps usually run at least 10C lower than my cpu temp, but my Phenom 9850 the core temp is always 10-15C warmer than the cpu temp.