We investigate the thermal conductivity of liquid water using computer simulations of the TIP5P model of water. Our simulations show that, in addition to the maximum at high temperatures at constant pressure that it exhibits in experiments, the thermal conductivity also displays a minimum at low temperatures. We find that the temperature of minimum thermal conductivity in supercooled liquid water coincides with the temperature of maximum specific heat. We discuss our results in the context of structural changes in liquid water at low temperatures.