A small gas turbine engine with a compressor, a combustor, and a turbine located downstream of the combustor. The compressor and turbine are supported on a rotary shaft, and a main bearing is support on the rotary shaft, the main bearing being located in a hot zone of the combustor. The main bearing includes cooling air passages within the races to provide cooling for the bearing. A cooling air is diverted from the compressor and passed through the bearing cooling passages for cooling the bearing, and then the cooling air is directed into the combustor. The cooling air is also passed through a guide nozzle before being passed through the bearing to cool both the guide nozzle and the bearing. A swirl cup injector is sued to deliver the compressed air from the compressor and the cooling air from the bearing into the combustor, the swirl cup injector also acting to draw the cooling air through the bearing.