An analytical study is made of the convective flow field produced when a warm cylinder maintained at a fixed temperature above freezing is buried in saturated frozen porous medium. The flow field is shown to have a double cell pattern due to the density inversion of water at similar to 4 degrees C, with downward convection of heat dominating at cylinder temperatures of below similar to 10 degrees C and upward heat convection dominating at temperatures greater than this. The analysis uses a perturbation technique to determine the first-order convective correction to the flow and temperature fields around the cylinder for a quasi-static case. It demonstrates that the porous medium permeability and the cylinder temperature are the dominant factors in determining the point at which convection heat transfer becomes significant, with convection expected to be insignificant for Darcy permeabilies lower than 10(-5) m/s. The analysis also gives an indication of the rates of thawing occurring in different directions without resorting to numerical methods. The practical implications of a thawing pattern significantly different to that predicted by conduction theory only are discussed briefly with respect to the problem of differential thaw settlement of arctic pipelines.