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A theory of thermally activated domain wall motion is presented in which attention is focused on the functional form of the domain wall energy variation in the direction of motion. It is shown that in general the activation volume is magnetic field dependent, and not necessarily constant, as is often assumed. A simple power law form of the wall energy variation, due to sample inhomogeneities, is found to exhibit a ln (wall veiocity) against field slope which decreases with decreasing temperature as is observed in thin films. The usual assumption of a constant activation volume predicts a slope which increases as the temperature falls.