This paper presents numerical results exploring the periodically repeating laminar flow thermal transport in a parallel-plate microchannel with ultrahydrophobic walls maintained at constant temperature. The walls considered here exhibit alternating microribs and cavities positioned perpendicular to the flow direction. Results describing the thermally periodically repeating dynamics far from the inlet of the channel have been obtained over a range of laminar flow Reynolds numbers and relative microrib/cavity module lengths and depths in the laminar flow regime. Previously, it has been shown that significant reductions in the overall frictional pressure drop can be achieved relative to the classical smooth channel laminar flow. The present predictions reveal that the overall thermal transport is also reduced as the relative size of the cavity region is increased. The overall Nusselt number behavior is presented and discussed in conjunction with the frictional pressure drop behavior for the parameter range explored. The following conclusions can be made regarding thermal transport for a constant temperature channel exhibiting ultrahydrophobic surfaces: (1) Increases in the relative cavity length yield decreases in the Nusselt number, (2) increasing the relative rib/cavity module length yields a decrease in the Nusselt number, and (3) decreases in the Reynolds number result in smaller values of the Nusselt number.