This past week I've been sealing up all the joints in my house HVAC ductwork to improve its efficiency.
I've been using HVAC caulk, it's a kind of mastic that's made specifically for a lot of flex and expansion/contraction from the metal it's on. It's extremely pliable after it's dry (some say it never really cures) and is designed for a wide temperature range... you could just goop it all around there, it goes on with the consistency of bull snot but hardenes to be more like silly putty - that'd be perfect here, way better than typical silicone adhesive caulk.