The cooling of a pulsed theta-pinch-type fusion reactor after the burn by means of the introduction of a neutral gas layer between the main plasma and the wall is discussed in terms of a simple mathematical model. The model assumes quasi-static heat flow and pressure balance and takes account of the fractional ionization of D-T gas at various densities and temperatures. The main result consists of an estimate of the initial injected neutral gas density required to remove the heat from the burnt and quenched fuel plasma in a given time for given reactor conditions.