Cassini's Composite Infrared Spectrometer (CIRS) maps the thermal radiation emitted by cold surfaces in the Saturn system. By examining the shape of the emitted spectrum at relatively long wavelengths of 9 to 16 microns (roughly 20 times longer-wavelength than the human eye can see), the CIRS team can determine the temperature on the surface.
Both light and dark material are very cold, but ice is much more likely to sublimate at temperatures of 128 Kelvin than 113 Kelvin. In fact, over a period of a billion years, about 20 meters of ice is expected to sublimate at those temperatures. The cooler bright regions would only lose about 0.1 meters of ice in the same period. Ice sublimating from warmer, dark areas would re-condense to the surface all over the moon, but would be trapped" on the cooler brighter regions a process called thermal segregation. This process is most likely responsible for the presently extreme segregation of bright and dark areas on Iapetus but it doesn't explain how the dark part of Iapetus was darkened in the first place.