I believe this has been discussed before. The problem with heating a vessel that large is that the center of the vessel doesn't get as much heat as the bottom or edges. I suppose you could stir it to get a consistent temp, but you would greatly increase the chances of infection and oxidation.
I think you would get a more consistent pasteurization if you are doing it in small bottles or some sort of inline flash or heat pasteurization during transfer.
All that said, if you discover a way to eliminate the obvious issues, let us know. It would be nice to see a different method.
if you were going to try it, I'd suggest swirling, instead of stirring. you don't have to open it or introduce any possible contamination, as well as reduce oxygen introduction. But it would improve heat transfer, and make it more uniform.