Some dielectric grease probably works - temperature could be an issue but might be for other suggestions also, but also as mentioned if you are replacing with LED you won't have as much heat, and maybe it won't cause it to seize up anyway.
The grease isn't conductive, that is still a function of contact surfaces, but what it does do is seal out oxygen and reduces oxidation or other corrosive agents are sealed out as well, and does give you a little lubrication when you do remove it.
I used to fight corrosion on 12 volt plugs for vehicle trailer lights, seemed like every time you plugged the trailer in, whether it be a month since you last used it or 6 hours, they seldom seemed to work and you had to clean contact surfaces to make them work. Put dielectric grease on them at least 3-4 years ago and they have worked every time since then, it keeps moisture and oxygen off the contact surfaces, yet tight fit still allows sufficient continuity through contact.