Equipment designed for manufacturing or testing of materials at elevated temperatures is often open to and at the pressure of the surrounding ambient. Since, it is an open system, with an increase in temperature the gas phase is expected to expand. This causes reduction in the density of the gas phase within the components or samples contained within the equipment. This reduction in density is linearly proportional to an increase in the temperature. As a consequence, because of its direct dependence on gas density, the rate of gaseous heat flow in the free-molecular regime within these components or samples should exhibit a corresponding decrease with increasing temperature as well. An analysis of this effect conducted by incorporating the effect of temperature on density at constant pressure in the original Knudsen-Kennard formulation, showed that the rate of gaseous heat transfer in the free-molecular regime in an open system at constant pressure is expected to exhibit a reciprocal square root dependence on temperature in contrast to the square root dependence of a sealed system in which the gas density is independent of temperature.