I do use a grease. I use a very thin coating of CMC Silaramac brake caliper grease, which won't burn off, and slide the barrel in.
I use SS shim stock (.001 or .0015 depending on the tolerances), and thermal fit every upper/barrel I have. So many of the uppers I prefer aren't undersized, so shim stock takes care of that.
In my case, I use an Odin Works vice block and a heat gun. I prefer to have at least .0015" extra room in the upper before I slide the shimmed barrel in. The barrel extension is one helluva heat sink and you don't have much time.
As far as removing a thermal fit barrel, that thin coat of Silaramic grease, the vice block in my vice, and an old broom handle I cut off provides all of the muscle needed without any heat. I hold onto the barrel, use a dead blow hammer, and don't go full caveman....