A microelectromechanical (MEM) pump is disclosed which includes a porous silicon region sandwiched between an inlet chamber and an outlet chamber. The porous silicon region is formed in a silicon substrate and contains a number of pores extending between the inlet and outlet chambers, with each pore having a cross-section dimension about equal to or smaller than a mean free path of a gas being pumped. A thermal gradient is provided along the length of each pore by a heat source which can be an electrical resistance heater or an integrated circuit (IC). A channel can be formed through the silicon substrate so that inlet and outlet ports can be formed on the same side of the substrate, or so that multiple MEM pumps can be connected in series to form a multi-stage MEM pump. The MEM pump has applications for use in gas-phase MEM chemical analysis systems, and can also be used for passive cooling of ICs.