The heatpipe is not always hot at the other end. However, if you decide to buy a new cooler, you can usually get them at a much lower price on eBay.
Also, have you checked that the thermal compound is not worn out? It has a fixed life, and depending on what type of compound/pad used, it may need to be reapplied. In case you aren't aware, you need to be careful replacing it. The old compound should be wiped off with 99% isoproply alchol. I usually use a coffee filter for this. Never touch the heatsink surface or the CPU surface, as oil from your fingers can get into the microgroove and affect cooling performance. You must then apply the appropriate amount of new thermal compound to the processor or cooler surface.
The manufacturer may have a video on this. If not, Youtube or service manuals are your friends here. Post any questions or problems you run into.