An approximate theory is derived to compute the thermal resistances of flat plate micro heat exchangers whose surfaces are heated with uniform flux. It is demonstrated that the thermal resistance can be minimized by proper selection of uniform conduit geometry. Further reductions in the maximum heated surface temperature and in the heated surface temperature gradients can be achieved by varying the conduit's cross-sectional dimensions asa function of the axial coordinate. This paper illustrates that a conduit's shape can be customized so as to achieve desired objectives.