With what has failed so far, I'd say leave it outside and try again tomorrow when it's below freezing. The heat is probably transferring to both pieces and that doesn't help.
Thermal shock is a good idea. As thin as the barrel is it won't take but about an hour to cold soak that barrel. No need to wait until tomorrow. But with all that said the cold outside isn't really all that cold but if that fails, do you have any liquid nitrogen? Dry ice might work too. Heat it with your heat gun and dunk it in nitrogen or rub it with the dry ice. Short of all that it sounds like some impact time on the wrench. Weld a bit on it and use a battery powered impact gun.That’s a heckuva idea, thanks