Thermally compliant auxiliary power unit (APU) ducts arrangements, and associated systems and methods are disclosed. A system in accordance with one embodiment includes an auxiliary power unit exhaust, that in turn includes an exhaust flow conduit, a housing disposed outwardly from the conduit, a support providing a load path between the conduit and the housing, and a baffle positioned along the flow conduit. At least one of the support and the baffle can have a resilient, radially compressible portion between the flow conduit and the housing.