one core runninig 10 degrees hoter than the other one

ihog

Distinguished
That sounds about normal since it's been 8 years. If it's too hot, then:

1. Buy thermal paste. (Arctic Silver 5 or Arctic Cooling MX-4 are sold choices)
2. Remove heatsink.
3. Clean processor's IHS (metal on top) and the heatsink with isopropyl alcohol and a lint-free rag/cloth/etc.
4. Place a dot of thermal paste in the center of the processor's IHS.
5. Reseat the heatsink.

tim.png

^Size of the dot.