Some dies have cores of different temperatures but usually not over 10C difference. Doesn't matter what TIM you use.
If it's a stock CPU without mods, and it's over 10C... just RMA it already.
Soldering works fine, Intel simply forgot how to do it anymore
It has worked before fine and it's working fine on all AMD CPUs.
Intel's IHS and TIM jobs even with paste are pretty bad. That's why many people go delid it to fix the stupid design/manufacturing errors. IHS too high, poor TIM, poor IHS flatness, ...