The efficiency of a crystalline silicon solar module decreases as its operating temperature rises. Module cooling is possible via selective reflection of sub-bandgap photons so that they are not parasitically absorbed. Selecting from a library of common dielectrics, we numerically optimize the design of two-layer mirrors at the outer glass surface of a crystalline Si solar cell module. The mirrors are designed to maximize the annual energy yield of a module by both reflecting light below the bandgap and enhancing the transmission of light above the bandgap. Combined ray-tracing and finite element simulations determine the power output and temperature of the module over time. Since any two-layer mirror would replace a conventional single-layer glass anti-reflection coating on the module glass, we study the ability of a two-layer structure to improve on a single-layer coating. The best two-layer designs improve the annual energy yield over a module with a glass anti-reflection coating and reduce the module operating temperature.