Even if the CPU is running in full performance all the time, it should not be overheating like this. When I transcode video on my Dell (transcoding is one of the more demanding tasks I do) the system goes to near-100% utilization, but does not get anywhere near this hot.
When it's doing nothing, the worst your temp should be is in the 35 - 45 deg C range, dependent on processor type.
Go look up the teardown instructions for your machine (try the vendor's website first). These should address how to get at the heatsink, Follow the directions carefully, clean the fins carefully (so as not to bend or break fins), and DON'T lift the heatsink from the CPU unless you have the right stuff to replace the thermal coupling material. Some vendors use paste, others use this phase-change material that can bond to the die of the CPU. If it gets stuck tightly enough, you could damage your system trying to get it apart. Go slowly, and don't pry on the sink trying to free it - you can strip the CPU out of the socket that way.
If your heatsink uses heatpipes (most of them do) check for cracks or breaks, as these will impair the sink's efficiency.
What kind of machine is it we're talking about, anyway? There may be a downloadable tech manual for it that shows the right way to do this, and tells you what sort of thermal coupling material is in use.
Easy does. Take it slow and carefully, especially since it seems to be your first time through this. That will get you there with success.