Dielectric grease probably won't help much, it won't improve the contact resistance. It's actually an electrical insulator (that's what "dielectric" means); its job is really just to keep moisture out. It's a long-term preventative, not a cure.
If you can't replace that plug easily, clean the contacts as well as you can using a small file, pencil eraser, scraper of some sort, even a small piece of fine-grit sandpaper. Nice shiny bright copper/brass contacts should be your goal. The male contacts should have some sort of bulge or projection to create some spring force to ensure good contact with the female contact in the cord; check if these have been smashed flat, and if so, try to bend them back again to restore some spring force. Spray some contact cleaner in there, then insert the cord end in and out (with the cord not energized!) several times, hopefully helping to scrub the contacts cleaner. Also make sure you get the cord plugged in ALL THE WAY when you start charging. Maybe it's backing off a bit and you're losing contact.
If none of that helps, if the contacts are bright and shiny and you're sure you've got a good connection, but you still get heat, the contacts probably aren't the problem. It's probably the connections TO the bike plug, which are probably crimp joints. If you have a bad crimp, it'll need to be fixed. Maybe you're got a friend who's an electrician who can help you out?