Hi Mate ! I have always had this issue with the pump. It is uncomfortable or painful, and also can constrict the blood flow to the penis and prevent it from responding to the vacuum. Find some comfortable way to tie back the scrotum. I have mainly used a silicone cock ring. I got a packet full of the ones which are supposed to tickle the lady, and cut off all the tentacles. The rings are very elastic, and can hold back the nuts gently without cutting off the blood flow.
Recently I have found these hard to get, and started using the narrowest available leather ball stretcher. It is simply a leather strap about 3/4 inch wide, which snap fastens around the scrotum. It took a few weeks to soften and become comfortable, but is now perfect for the job.
There are other alternatives you could try. Perhaps theraband, or a hanky, could be used to tie up and hold the nuts down. Whatever you use does not have to be tight, just comfortable and snug.
I also found it helps not to get any lube on the scrotum; this just makes it easier to slide into the tube. Originally I used to pump up the pressure, then pull the scrotum out, and put on the ring. Now I put on the ring first and rarely get any skin in the tube.
If your blood flow to the penis is adequate, I think it should feel warm not cold. I think this issue will probably resolve if you find a way to keep the scrotum skin from going in the tube.
Best
Kit