If the dielectric grease is same as thermal compound, and I am not sure it is, but if it is under a period of time it dries out.
I have retired my Win XP Pentium 4 processor PC from being used on the internet, but at one time I cleaned the dust out and removed the processor from the heat sink and cpu fan.
The heat sink was held on quite fast to the cpu top with what else, thermal compound grease. I think heat and a length of time it gets gummy.
I have resorted to using dry lock ease powder graphite. I empty a small pile in a cloth and run the cable through the graphite a few times and it sticks to it.
I then put the cable into the cover and pull it out to re-coat the cable again, as the cable coating of graphite gives up some of the graphite coating to the inside of the cover.
Once more of this process and it is done. Cold or heat it seems to be doing well for me.
I even used it on the recoil starter rope. It is a bit messy for that application as you might handle the cord during a repair, but it washes off easy.