Unfortunately air is an excellent insulator. I looked it up and helium has thermal conductivity and heat capacity about 5 times higher than air. So significant

Unfortunately air is an excellent insulator. I looked it up and helium has thermal conductivity and heat capacity about 5 times higher than air. So significantly better but we have to remember that solids have something like a thousand times better thermal properties than gases and it is the solid bits we are mostly concerned with. So it really depends on where the heat is originating in the drive. I suspect the big advantage is the lower viscosity of helium which prevents heat generation in the drive cavity in the first place.