The temperature driven gas flow in a two-dimensional finite length microchannel and a cylindrical tube are studied numerically with the goal of performance optimization of a nanomembrane-based Knudsen compressor. The numerical solutions are obtained using direct simulation Monte Carlo method and discrete ordinate method for BGK model kinetic equation in a wide range of Knudsen numbers from 0.05 to 50. The length-to-height ratios from 5 to 30 were examined. Three different wall temperature distributions were considered, namely, linear, stepwise, and a non-monotonic profile typical for a radiantly heated Knudsen compressor membrane. The short channel end effects are characterized, and the sensitivity of the mass flow rate to a non-monotonic temperature distribution is shown.