The concentrated solar thermal industry is moving towards higher temperature receivers. Gas-phase receivers represent a near-term solution that can achieve such temperatures, but most designs for pressurised receivers require a window. The window represents the weak link in the designs, limiting a receiver’s operational life, temperature, and pressure. Indirectly-irradiated receivers, which do not require a window resolve these issues, but introduce a detrimental performance trade-off because solar energy must be effectively conveyed through a solid receiver wall. This can result in a lower thermodynamic efficiency (first and second law) since there is a large difference in temperature between the inside and outside of the receiver wall. To deal with these issues, this paper investigates novel, indirectly-irradiated receiver designs with the potential to reduce the temperature drop across the receiver wall. The proposed new type of cavity absorber was designed by first considering its optical performance via a detailed ray-tracing analysis. These results indicated that a cylindrical cavity with an inverted conical base provides the highest optical efficiency, around 92%, compared to other cylindrical cavities with different base shapes. Next, to reduce the temperature drop in the design, heat transfer enhancements for the cavity wall were explored using the ray tracing-calculated radiative flux. It was found that a compound technique of impinging jets on an extended surface enables more design freedom while also providing higher convective heat transfer coefficients compared to either technique alone. To explore the range of heat transfer enhancements that are possible with these methods, this paper also presents parametric performance maps of heat transfer coefficients and pressure drop as a function of nozzle-to-cavity distances, nozzle diameters, and the number of nozzles. According to this analysis, a design with around 48 nozzles per square metre, each of 9 mm diameter, around a metal foam-covered cavity, achieved the optimum design point with respect to the overall heat transfer efficiency. Overall, it was found that an optimally designed indirectly-irradiated gas-phase receiver can indeed provide high performance and can potentially enable solar systems to reliably operate at well above 600 °C for driving advanced thermodynamic cycles.