Thermal energy storage in a phase-change material due to latent heat of fusion caused by conduction-controlled melting during radiative heat injection is considered. It is solved employing variational, integral, and quasi-steady methods. They yield closed-form solutions which are functions of the Stefan number, St, and the surrounding temperature. The results for the design parameters for the storage system obtained from these methods exhibit insignificant variation and are unaffected by the surrounding temperature, theta(a), for St < 0.1. The second law efficiency for this storage is devised. It is insensitive to changes in St and the heat absorption depth, eta(m), for theta(a) less-than-or-equal-to 1.2.