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A mechanism for a microfluidic pump that leverages alternating adverse and favorable thermocapillary stresses along menisci in a (periodically) fully developed transverse flow in a microchannel is exemplified. The transverse ridges are the interdigitated teeth of cold and hot (isothermal) “combs” and free surface menisci span the interstitial regions between them. The teeth are asymmetrically positioned so that the widths of adjacent menisci differ. This architecture is essentially that of the theoretical pump proposed by Adjari [Phys. Rev. E 61, R45(R) (2000)] but exploits thermocapillarity rather than electro-osmotic slip to drive unidirectional pumping. A theoretical model of the multiphysics pumping mechanism is given that is solved in closed form. Two explicit formulas for the pumping speed are provided. One is derived from the exact solution to the full problem; the other follows from the reciprocal theorem for Stokes flow combined with an exact solution to a distinct problem resolving apparent slip over superhydrophobic surfaces [D. G. Crowdy, Phys. Fluids 23, 072001 (2011)]. A conceptual design of the pump is also outlined; this involves no moving parts, requires no external driving pressure, and pumps a continuous stream of liquid through a microchannel, as opposed to a series of discrete droplets. Since there is only a periodic component of the pressure field the microchannel could be made arbitrarily long and the menisci, which would be essentially flat, are more robust than for conventional pressure-driven flow.