The vertical-external-cavity surface-emitting laser (VECSEL) has shown promise in becoming an efficient source of high power and high beam quality coherent radiation. In order to live up to its true potential, the VECSEL must be thermally managed in order to avoid thermal damage as thermal lensing and filamentation causing preventing it from operating in a single mode regime. For an optically pumped VECSEL, optical cooling presents an elegant solution for thermal management as it does not require electrical or thermal conduction. The goal of optical refrigeration is to achieve radiation balance lasing (RBL) when the active medium is maintained at a steady uniform temperature. In this work, we investigate the active medium characteristics and operating conditions that can lead to RBL in a semiconductor medium and show that to achieve RBL, the gain medium should be engineered to create a density of states that simultaneously allows gain and strong anti-Stokes luminescence. Such a medium may incorporate bandtail states, impurities or quantum dots. We provide a recipe for optimization of such band structure-engineered materials to achieve the lowest threshold and highest output power.