The paper describes a simplified approach to a method for calculating the temperature profile of a cooling river below a source of thermal pollution and the length of ice-free reach which could be maintained by such a source. Heat loss is calculated as a linear function of the difference between water temperature and air temperature, so that the integration can be performed analytically. A simplified but fairly general procedure for calculating water- air heat-loss rates on the basis of air temperature, windspeed, solar radiation, and general atmospheric conditions is also presented.