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Here's what I have found works best and is safe:
- Release the clips holding the cooler on.
- *WAIT* Let it sit for a few minutes.
- Do not pull on the heatsink!!!
- Instead, twist it gently with it still sitting loose on the socket. It will be sticky because of the bond between thermal paste and CPU heat spreader with no air bubbles. Rotate it as far as it can go easily without bumping into motherboard components. Reverse the twist direction and go back the opposite direction as far as you can. You may need to repeat this twisting motion back and forth a few times.
The twisting motion minimizes stress on the CPU pins and will help break the bond between the old thermal paste and the CPU.
It introduces micro-pockets of air as you rotate the heatsink on the thermal paste. It will eventually loosen up and be very easy to lift the heatsink off.
Do not rush it or you risk forcibly yanking the CPU out of the socket or breaking off a pin.