brass starts to seriously anneal at about 430 degrees, and will actually start to soften at a lower temperature. Some forms of brass start to anneal at 220 degrees. The annealing process is normally restricted to the neck and shoulder areas of a case, and the process will continue unless the heat transfer is stopped. I like to shock my cases in ice water, but I suppose there other methods out there. here is also a time frame for heat saturation and in this case a brass cartridge case. The real issue besides heat is the very thin form of the brass; making heat saturation very short in time. Heat is brass and aluminum moves very fast thru the metal, and this is a serious issue to be taken into thought. Taking the metal out of the heat, and letting it just stand there will only help the heat transfer to the parts we don't want to soften. You must stop the heat from moving in the metal!
Now in this case the cases are probably trashed. 350 degrees is right at the bottom of the annealing window, but also there was a length of time to add to this. Plus the entire case was heated. Perhaps you could run the thru the full length die several times to work harden the brass, but I doubt that will be the case (not a pun). Even then your going to need to fire the cases each time, and I'm not all sure I'd want to do that. With the bottom half of the case now softened, they may well be dangerous to shoot.
gary