A new approximate method is developed for calculating the temperature distribution in an atmosphere where local mechanical-energy dissipation is balanced by local net radiative loss in one or more spectral lines for which the atmosphere is optically thick. The method uncouples the equations of radiative transfer for the individual spectral lines from the energy-conservation equation and from each other. This permits a solution of each individual transfer equation for the radiation field in each line. These results, used in the energy-conservation equation, yield the temperature distribution if the optical depth ratio of the spectral lines at each point is known. The method is applied to selected strong resonance lines in the solar chromosphere.