Large temperature difference between the cores, under load - why?

Question

Processors

Bought for aliexpress xeon e3 -1220 v3. The temperature difference at the same 100% load on all cores reaches 20 degrees. In idle - 3-4 degrees.
Do I understand correctly that the thermal interface under the processor cover has turned into a ram, and scalping with the replacement of the thermal interface is desirable?
In general, it is somehow strange that in such small volumes there is no redistribution of heat ... The temperature of the package is almost equal to the temperature of the hottest core, and the coldest core is 20 deg. below. Well, for example, 75 and 55.

Answer 1

You understand quite rightly, heat is unevenly removed from the processor cores to the heat-distributing cover. Alternatively, it is also possible that you installed a skewed cooler, this also contributes to similar problems.

Answer 2

The option with a cooler is excluded, the situation is repeated on different coolers, the processor cover is even.
I just hoped that such an option might be possible that "the sensor has gone crazy", but this does not seem to be the case.