Intel Core i7 cores have different temps

[darkstar845]

Should I be concern about the 7-8 degree difference between core 0 and core 3?

 

[Scotteq]

Some difference is normal, since the mating surface to the HSF is never really perfect and because different cores may be presented with different loads. My own system is 2~5 degress different between cores. So yours isn't all that out of line.

At most, you may want to remove the heat sink/fan, clean the respective surfaces, reapply TIM, and re-mount. But as long as your overall temps are under control, I don't feel it's necessary. But if you're like me, this kind of stuff tends to sit in the back of your head and fester. So... certainly wouldn't hurt.