If you're using one of the AVCHD camcorders keep in mind that when shooting video to a flash memory card, the mts files get broken up into 4GB chunks. These have to later be stitched together or there will be skips at the point a new file is created.
This is standard and actually not a big deal to do with editing software, (or the provided SW included with your camcorder), but it is an extra step and could be time-consuming if you are dealing with a large amount of data/as it seems you may be from your post.
I have never used one of those external recorders but if the device makes your recordings into one, seamless file for each video take this may be a clear advantage for your situation.
Regarding overheating, you shouldn't have a problem with a camcorder two hours at a time. If you get a DSLR; yes, there may be a problem with overheating. The exception to this is the Panasonic GH2 or GH3; although technically "micro-four thirds" cameras, they are inter-changeable lens cameras that are casually referred to as DSLR's and won't overheat as a DSLR might with long shoots.
But camcorders definitely shouldn't be used as a surveillance camera might/for many hours; they are intended to be used "intermittently". I don't know what your depositions typically involve, but if it's always one fixed angle, you could get a good surveillance camera. some that have zoom lenses, that are designed to be on 24/7 and overheating would definitely not be an issue.