A cracking furnace includes a combustion volume defined in part by a burner wall having a refractory lining. A plurality of perforated flame holders is arranged in an array that is spaced away from the wall, with fuel input faces facing the wall. Each of a plurality of fuel nozzles is positioned and configured to emit a fuel stream toward the input face of a respective one of the plurality of perforated flame holders. Combustion reactions, supported by the fuel streams emitted by the fuel nozzles, and held by the flame holders, release heat, which is emitted by the flame holders as thermal (blackbody) radiation, a portion of which impinges upon, and heats the inner face of the refractory lining. Thermal radiation from the flame holders and the wall impinges upon a load positioned in the approximate center of the combustion volume, between burner walls.