Could it be from kicking at flies under his belly or sheath? That is hard work - I have one gelding that sweats more on one side than the other in the location you mentioned, from kicking at flies. If his feet are cool I wouldn’t stress yet.
It might not be a bad idea to put what you have on hand on those soles if you’re worried - wrapping the fronts after an application of Durasole, Magic Cushion, or even some poultice might offer some short term relief. There’s always a transitional period when shoes are pulled.
I’ll keep jingling for his continued recovery! And @cayuse how is your mini doing?