Had a similar experience with a JBOD chassis. The vibrations of the spinning drives caused resonance on some positions. The cure was to attach a patch of duct tape with a washer at a certain point on the chassis.
My previous PC had the option of inserting harddisks in rubber bands instead of screwing them to the frame. It was a case specifically aimed at noise reduction (the Antec Solo).
That sounds like a really easy way to make a hard drive overheat.
Way back, I had a 4GB SCSI hard drive that was extra tall, extra fast, extra noisy, and extra hot. I constructed a thick rubber box around it to try noise-proof it a little, but I also had to strap a CPU cooler to it and have the airflow enter the box and exit at a hole in the box after wrapping all the way round the hard drive. It worked. But just wrapping it in rubber would have been a very quick way to cook the drive. This is a drive that if just left running bare on a table would get too hot to touch.
Hard drives produce a heck of a lot less heat these days.
An elastic mount does not have to be a suffocating box.
Plus, and I could be wrong here - the mounts are not really designed to be heat conductors (the rails are plastic on my high end Dell workstation); I suppose the heat is extracted via air flow.