Athlon 7850BE

http://www.cpuid.com/download/hwmo [...] or_114.zip
use that, tell me what cpu temp and core temps are

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/Desk [...] &f10=&f11=

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

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'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.