We demonstrate the robust operation of a gallium arsenide tunable-barrier single-electron pump operating with 1 part-per-million accuracy at a temperature of 1.3 K and a pumping frequency of 500 MHz. The accuracy of current quantisation is investigated as a function of multiple control parameters, and robust plateaus are seen as a function of three control gate voltages and RF drive power. The electron capture is found to be in the decay-cascade, rather than the thermally-broadened regime. The observation of robust plateaus at an elevated temperature which does not require expensive refrigeration is an important step towards validating tunable-barrier pumps as practical current standards.