How important are core temperatures?

Could you post a link to that statement? Also, what model CPU do you have?
Check out the Core2Duo Temp Guide.

I personally consider any thing above 70C too dangerous and NOT OK. I don't listen to the Intel temp specs (except for TjMax). They are usually too high for my liking. Check out CopuTronix guide for more explanations,etc.
http://www.tomshardware.com/forum/221745-29-core-quad-t...

Sorry forgot to add the CPU is the Q9450.

I emailed them saying my CPU is running at 60C but the cores are close to 80C and they said "Your processor is running at 60 degrees Celsius, this is below the maximum recommended temperature for the CPU, again you do not need to worry about the temperature of the cores, just make sure that the temperature of the CPU does not go higher than 71.4 degrees Celsius."

I think what intel meant was it is ok for your cores to be running at 80C as opposed to rma'ing the cpu to us  

What cpu, I assume it is a quad q6x00 or q9xx0 and what cooling? And did they send you an email stating that?

Though they are just quoting the thermal specs, but given cpu temp may be a little off, with 80 core, you may be over thermal specs of cpu. Regardless, I would not tolerate temps that high.

Also, cant have 20C difference between core and cpu diode. my guess is you are using coretemp or everest or hwm for temps, which is using tjmax 105, which is likely 10 too high, and hence temps reading 10C too high. So your cores may only be 70C.

Yes I used coretemp. But 70C is still far too high though. That was stress testing for about 4 minutes so the temperature could raise quite a bit more after a few hours.

Try using Real Temp 2.5, no offsets required, will give you core temp and distance to TJMax, also provides logging options.

Are you sure you fully read the e-mail and did not miss something ??
check again, you must find the following mentioned somewhere
" If it smoked send us your money and we'll be more than happy to send you another one"
 

No, I wouldn't expect the temp to rise much higher. The core temps respond quite quickly.

It is NOT a good temp.You will fast start to get some errors.You must get it down to at least 60*C.My temp is 42*C idle,52*C under full load.How much is your motherboard temp?

For a 45nm chip its a bit stupid. I hope it will be much better when I get a new case and heatsink.

@OP: The best method for getting accurate temps are to follow the C2D Temp guide and calibrate SpeedFan or use a digital IR thermometer.