Solar thermal fuels (STFs) are an unconventional paradigm for solar energy conversion and storage which is attracting renewed attention. In this concept, a material absorbs sunlight and stores the energy chemically via an induced structural change, which can later be reversed to release the energy as heat. An example is the azobenzene molecule which has a cis-trans photoisomerization with these properties, and can be tuned by chemical substitution and attachment to templates such as carbon nanotubes, small molecules, or polymers. By analogy to the Shockley-Queisser limit for photovoltaics, we analyze the maximum attainable efficiency for STFs from fundamental thermodynamic considerations. Microscopic reversibility provides a bound on the quantum yield of photoisomerization due to fluorescence, regardless of details of photochemistry. We emphasize the importance of analyzing the free energy, not just enthalpy, of the metastable molecules, and find an efficiency limit for conversion to stored chemical energy equal to the Shockley-Queisser limit. STF candidates from a recent high-throughput search are analyzed in light of the efficiency limit.