Micro combustion and power generation systems have increasingly been investigated as potential alternatives to electrochemical energy storage thanks to hydrocarbon fuel's high energy density, but electrical componentry for pumping significantly limits the overall system efficiency. These components must be eliminated to allow for widespread adoption of micro combustion and power generation systems, and so the development of an alternative pumping technique is required. By taking advantage of the thermal transpiration phenomenon, small-scale pumping can be obtained in the presence of a temperature gradient. Initial work has been done to investigate the efficacy of this system, but a major issue has arisen due to the lack of low-cost thermal transpiration membranes with desirable pore characteristics. Research has revealed that vessel hyphae present in the roots of mushrooms (mycelium) form a network which could meet the requirements of an effective thermal transpiration membrane. Proper growing conditions could also allow for an application specific mycelium structure providing a highly effective and low-cost thermal transpiration membrane for micro combustion systems.