I've never had to change an HSF before, I'm curious as to whether doing so causes any problems. For example, does the thermal paste cause the HSF to stick to the CPU, or should it the HSF assembly just lift off without any problems?
The cooler often sticks to the CPU. Many coolers come with thermoplastic material that softens when warm, so the best method is to remove the cooler right after shutting the PC off.
To break it loose, it's often necessary to twist the cooler slightly after removing its retention clip.