What heat-resistant rubber could I buy?

Silicone is the elastomer with greatest temperature resistance. There's an obscure elastomer called Sifel from Shin-Etsu which also has high temperature resistance. It's a perfluorinated carbon backbone with silicone end-groups. It's available with curing mechanisms similar to silicone, such as A/B part thermal cures.

Gold has about the least adhesion to anything.

Silicones and Sifel are not known for good adhesion, but "adhesion packages" (principally silane coupling agents) can greatly improve adhesion, but this is adhesion which develops during cure. The best adhesion is when the elastomer cures in contact with the metal.

A silicone caulk would have an adhesion package. A clear caulk would be unfilled. I believe there are silicone caulks sold for sealing the joints between the panes of glass aquaria that might work for you. Sifel is also available in formulations with good adhesion, for example to attach lightbulbs to bases.

Silicones are well-known for out-gassing low molecular weight oligomers which can contaminate vacuum systems. They can leave films which further contaminate anything that subsequently goes through the vacuum system. This surface contamination can adversely affect electrical contacts, adhesive bonds, thermosonic welds, etc. Don't say you weren't warned!

First of all thanks for the answer. I did not know that silicon under certain conditions is elastic. I have read through the Wikipedia entry for silicon and found there that it is even used for bouncing balls; and one can think of other examples. I imagine that a thin (quarter of a mm thick) layer of the same kind of silicone would be easy to stretch.

It is a suggestion on which I can work. With a little bit of ingenuity I could figure out a way of obtaining a sheet of material out of the caulk. Also thanks for the warning about the outgassing. I was thinking of doing the deposition on a sputtering system, which does not need high vacuum, but I will check this carefully.