In this research, numerical simulations are used to analyze the mean free path distribution of a (highly) rarefied gas hosted in a constant temperature model cylinder. In the Knudsen regime, gas-gas collisions do not occur and molecular transport can be fully attributed to gas-wall collisions. It is commonly accepted that the mean free path probability distribution then becomes highly nontrivial. Therefore, we propose to analyze this function in terms of its first two moments. We show numerically that both the first and second moments of the path distribution are important in describing the transport of a rarefied gas. In case of the Smoluchowski thermostat, a thermal wall mechanism for the cylindrically shaped pore, the obtained values can be compared with the results that follow from kinetic gas theory.