We analyze a heat engine based on a hot cavity connected via quantum wells to electronic reservoirs. We discuss the output power as well as the efficiency both in the linear and nonlinear regime. We find that the device delivers a large power of about 0.18 W cm-2 for a temperature difference of 1 K, nearly doubling the power that can be extracted from a similar heat engine based on quantum dots. At the same time, the heat engine also has good efficiency albeit reduced from the quantum dot case. Due to the large level spacings that can be achieved in quantum wells, our proposal opens a route toward room-temperature applications of nanoscale heat engines.