A co-fired generator for use in a continuous-cycle absorption heating and cooling system may provide heat to the interior of an annulus chamber from a first heat exchanger, such as a firetube heat exchanger, supplemented by heat to the exterior of the annulus chamber from a second heat exchanger containing fluid heated by an external source. Some embodiments may circulate fluid heated in a solar-heated collector through the second heat exchanger. Other embodiments may route exhaust gas from a combustion engine through the second heat exchanger. The second heat exchanger may be provided with a plurality of fins to increase the surface area available for thermal transfer between the heated fluid and the annulus chamber.