I don't know for sure. My best guess is they have a calorimeter, a device which measures the irradiance on a surface. The Bodybugg companies then does a series of calibrations to convert the irradiance into the power the body outputs. The power used per (second?) is integrated up over the course of a day, and converted into calories.

Essentially, it's a fancy thermometer.

Never heard of such a device. You really do learn something new everyday!