We have monitored the temperature field within first-year sea ice in McMurdo Sound over two winter seasons, with sufficient resolution to determine the thermal conductivity from the thermal waves propagating down through the ice. Data reduction has been accomplished by direct reference to energy conservation, relating the rate of change of the internal energy density to the divergence of the heat current density. Use of this procedure, rather than the wave attenuation predicted by the thermal diffusion equation, avoids difficulties arising from a strongly temperature dependent thermal diffusivity. The thermal conductivity is an input parameter for ice growth and climate models, and the values commonly used in the models are predicted to depend on temperature, salinity, and the volume fraction of air. The present measurements were performed at depths in the ice where the air volume is small and the salinity is nearly constant, and they permit the determination of the absolute magnitude of the thermal conductivity and its temperature dependence. The weak temperature dependence is similar to that predicted by the models in the literature, but the magnitude is smaller by ~10% than the predicted value most commonly used in climate and sea ice models. In the first season we find an additional scatter in the results at driving temperature gradients larger than ~10--15 ¿C/m. We suggest that the scatter arises from a nonlinear contribution to the heat current, possibly associated with the onset of convective motion in brine inclusions. Episodic convective events are also observed. We have further determined the growth rate of the ice and compared it with the rate explained by the heat flux from the ice-water interface. The data show a sudden rise of growth rate, without a rise in heat flux through the ice, which coincides in time and depth with the appearance of platelet ice. Finally, we discuss the observation of radiative solar heating at depth in the ice and demonstrate that the absorption exceeds that in the ice alone; dust or algae must contribute to the absorption. ¿ 2000 American Geophysical Union