We present an analysis using conventional heat-transfer theory of a common type of synchrotron-radiation-beam-line mirror with rectangular cooling channels. The analysis leads to a simple analytic expression for the slope error, which enables the distortion performance to be estimated in practical situations. It also provides an understanding of the effect of the various parameters on the goodness of the cooling process and an insight into the underlying physics. The analysis is applied to determining the design steps needed to achieve low slope errors and/or high-heat-removal rates with this type of mirror. The slope-error performance of various materials in a specific design are compared and the best performance is obtained from (in order) invar, silicon, and silicon carbide.