One company I bought heated grips from in the past recommended a two part epoxy for cementing the grips on but not the fast drying type because it has a lower temperature threshold and would soften from the heat of the grips. They did sell their own product but were open about the fact that you didn't need to buy it. They said to just use a two part epoxy like JB Weld that takes overnight to cure because it has a higher temperature threshold than the quick drying type. They specifically said that silicone was one of the products to be avoided for the reasons that you are experiencing. I used JB Weld and never had a problem.
From their website;
EPOXY: We recommend only slow curing (generally considered 6+ hours, or overnight) two-part epoxy because it is usually rated at 250 degrees F. The quicker curing epoxy is generally rated at 200 degrees F or lower. Do NOT use silicone sealant, crazy glue, at 200 degrees F. Do NOT use other types of adhesives. DoNOT use silicone sealant, crazy glue, superglue, other superglue, other cyanoacrylate adhesives, weather-strip adhesives, or anything else. Just use two-part epoxy of the type we recommend. There are many brands out there, and some of them are DURO, DEVCON, JB WELD, BORDEN, etc. Most are available at auto parts stores, hardware stores, and often found in “Big Box Store” hardware or automotive departments. (The reason we do not want you to use anything other than epoxy is because of the temperature these grips may reach in service, and because other types of adhesives rely on solvent evaporation, which may take a very long time. Most other adhesives will soften with elevated temperatures, and you don't want these grips to loosen while riding.)