  Within the t-J model, the heat transport of the underdoped cuprates is
studied based on the fermion-spin theory. It is shown that at low temperatures
the energy dependence of the thermal conductivity spectrum consists of two
bands. The higher-energy band shows a weak peak, while the low-energy peak is
located at a finite energy. This high-energy broad band is severely suppressed
with increasing temperatures, and vanishes at higher temperature. It is also
shown that the temperature dependence of the thermal conductivity increases
monotonously with increasing temperatures, in agreement with experiments.
