Adhesive tape to affix rubber to carpet in high temperatures?

I've tried google and I can't figure out what to search for. So far I've tried duck tape, gorilla tape (from the makers of Gorilla Glue) and true duct tape. The duck tape and the gorilla tape work great...until it heats up and they melt. The duct tape doesn't stick to the carpet.

(and because I know you are wondering- I have 300 rubber ducks in the back window of my car, currently they are affixed with duck tape but it keeps melting and i keep having to reattach them.)