An analytical and numerical investigation of the transport of thermal neutrons in a hot moving medium is presented. The analytical portion of the paper develops solutions to several idealized problems which are then used in the numerical section to validate the computer program and technique used for making calculations of realistic problems. An example of a realistic problem is presented involving a shallow buried strong explosion accompanied by the release of neutrons. The fraction of neutrons captured in the soil which has been lofted above the original ground surface is determined. Also obtained are the fractions captured in soil below the ground surface and in the air above the ground surface.