If possible, may want to try flashing the bbb with the latest pristine 05/08/13 angstrom image, using a power adapter with recommended ratings: 5V 2A. 'am not electronics expert, but the lower recommended amp rating may be safer. If that works, then reflash with the pristine 13.04 ubuntu image. If that works, it could imply that the ubuntu upgrades were causing the high temps & freeze.
Myself and I think some others too, have found that the processor gets quite hot to touch, when doing a opkg upgrade of the Angstrom image. It did not freeze due to overheating and I did not measure the actual temp. But it was very high to the point that touching it for about minute was intolerable.