Thermal permeation, or thermo-osmosis, is the flow of a fluid through a membrane having a temperature gradient imposed across it. For the system, gas + polymer membrane, the approach of the pressure difference to its final steady value is expressed as a function of time for both a differential and an absolute manometer. The derivation assumes a quasi-steady state at all times but restrictions imposed on the previous treatment have been lifted. The final equations show a logarithmic dependence of a ratio of pressure differences on the time, which was only previously valid for a special case. They indicate that though the change of volume of a gas reservoir may be much less than the actual volume, the fact that volume changes at all can still significantly alter the relaxation time for the approach to steady state.