The camera body of the Hero3 and the Hero3+ is identical, they both will fit the Freedom360 mount just nicely... The FoV of the lenses are also very similar. GoPro claims 30% longer battery life, and we are testing this claim at the moment, as well as the heat profile. (Much of the heat of the GoPro cameras is radiated out of the front, which is why the F360 doesn't cover the front as a heat sink surface).
We found no support for the general claim that every Hero3 overeats all the time. Some of the early Hero3 (late 2012 models) had production issues, which caused them to overheat and shut down. It was easy to spot this erratic behavior, and return the cameras right away. From our experience, the production quality got much better in Spring/Summer, we we didn't see that problem anymore. We had been using H3B for all kinds of productions, including recording concerts on the Summer Stage in Central Park (NYC on a hot day), recording 2h uninterrupted (with external power attached) and without any crashing/rebooting/overheating etc. We do expect the H3B+ to be even more reliable in that regard. GIven the numbers of H3B out there in the world (probably 1M+), systematic failure would cause much larger uproar in the online forums.
The only thing that has changed with the new Hero3+ in regards to size, is the waterproof acrylic housing, which is indeed about 30% smaller.