Recent experimental and theoretical studies of heat-recirculating combustors have demonstrated the importance of thermal conduction through the structure of the combustor on its performance. In particular, this solid-phase heat conduction inevitably degrades performance via transfer of heat out of the reaction zone to the surrounding structure, which is then lost to ambient. This in turn leads to a reduction of reaction temperature and thus sustainable reaction rates. By use of platinum-based catalysts in spiral counterflow "Swiss roll" heat-recirculating combustors, we have been able to sustain nearly complete combustion of propane-air mixtures at temperatures less than 150°C using combustors built with titanium (thermal conductivity (k) of 7 W/m°C). Such low temperatures suggest that high-temperature polymers (e.g. polyimides, k ≈ 0.3 W/m°C) may be employed as a combustor material. With this motivation, a polyimide Swiss roll combustor was built using CNC milling and tested over a range of Reynolds numbers with propane fuel and Pt catalyst. The combustor survived prolonged testing at temperatures up to 450°C. Reynolds numbers as low as 2 supported combustion, with thermal power as low as 3 watts and temperatures as low as 72°C. These initial results suggest that polymer combustors may prove more practical for meso- or microscale thermochemical devices due to their lower thermal conductivity and ease of manufacturing. Applications to electric power generation via single-chamber solid oxide fuel cells are discussed.