GE Silicone number one is heat-proof over 400F. You could actually just form a new rubber cap from a blob of that stuff.
And that might actually be safer since the original rubber might possibly react poorly to silicone. It really depends on what it is and we have no way to tell that.
Years ago I worked in the glazing industry and we did many long-term evaluations of silicone sealants on various kinds of synthetic rubber and rubber-like things.
What we found out was that in the long-term most common forms of non-silicone synthetic rubbers were subject to degradation. On the other hand most of them also degraded just from time and exposure.