I'm going to say that since the OP says he recently MOVED the PC and suddenly has a significant jump in temps, we're probably looking at a mechanical failure of the CPU HSF mount or damage to the cooler itself. Dismount the HSF and backplate then inspect to make sure none of the mounting points have failed. Assuming everything looks good, remove the old thermal transfer compound from the CPU and HSF with a coffee filter + 90% alcohol, apply a rice-size dab of AS5/Ceramique to the CPU, buff a small quantity into the bottom of the HSF, re-mount - power up. Taking into account any changes in the baseline ambient temps in your new environment, test your cooler at idle and under load to ensure it is performing properly before investing the time and effort lapping. If you cracked a heatpipe or otherwise damaged the cooler during the move there's not much point to lapping, particularly if you decide to RMA it back to Tuniq.
Since the Tuniq coolers are notorious for having a rough interface surface lapping would be of benefit if you have the right equipment. Keep in mind that if you do it wrong and either make the surface uneven or remove too much material you will actually hurt your cooler's performance, so weigh the risks versus your patience and skill.
If you've never lapped a heatsink before it's important to use a flat, smooth surface like a marble flooring tile or 1/2" glass plate with sandpaper or polishing compound applied to the surface for lapping rather than trying to polish it free-hand. A majority of people who try to free-hand lap (sandpaper in one hand, heatsink in the other - rub together furiously) a heatsink will do it wrong and either result in a net 0 gain or make the cooler's performance worse.
If you use sandpaper (I like the black stuff with a bit of water, preference varies from person to perosn though) use duct tape on all 4 sides of the sheet to secure it to the tile and ensure it doesn't shift while you work. Cover the bottom of the heatsink with black permanent marker and as you are removing material with progressively higher grit paper, keep checking to make sure you are removing it evenly. If you're doing it right, the marker should disappear from the bottom of the lapped heatsink evenly, if not you will need to carefully adjust the pressure you are using to compensate. Once the marker is gone and you've gotten to the highest grit sandpaper, tape a buffing cloth to the tile and then use metal polish to get a mirror shine.
There are different techniques out there so do lots of reading on the various O/C sites that document the process and try a practice run or two with a non critical heatsink if you can. Old northbridge heatsinks or VGA coolers are always prime candidates.
Good luck!
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