For the conversion of absorbed sunlight into useful thermal power, we demonstrate that the profiles of absorber temperature, fluid temperature and thermal power delivery along linear solar collectors can be solved in closed form even when the collector heat-loss coefficient is far from constant over the collector operating range. This analytic solution eliminates the errors inherent in earlier approximate solutions, and makes the dependence of collector performance on component properties transparent. An example for a realistic solar concentrator illustrates the improvement in prediction accuracy.