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This paper investigates the topology optimization of planar cooling channels using a low-cost multilayer thermofluid model. A novel three-layer model including the upper/lower cover-plate layers and the central solid-fluid mixing layer is proposed. The flow boundary layer effect and the heat transfer effect in the thickness direction are modeled as the flow coupling and thermal coupling effects between adjacent layers, respectively. Particularly, in order to estimate more accurate temperature fields, the constructed three-layer heat transfer model in the solid-fluid mixing channel is derived based on the assumption of adaptive temperature profiles in the thickness direction. Further, based on the three-layer thermofluid model, the porosity field is introduced to describe the channel's topology, and the corresponding topology optimization scheme is presented. Several optimized channels under different constraints and boundary conditions are shown and discussed in comparison. Optimized channels show streamlined boundaries and reasonable layouts and exhibit competitive heat dissipation performance. Parametric studies are conducted to analyze the effectiveness and reliability of the topology optimization scheme. Further, to evaluate the accuracy and efficiency of the proposed three-layer model, optimized channels are simulated with the full 3D model and previous low-cost models. The proposed three-layer model exhibits good consistency with the full 3D model while achieves great improvement in efficiency. [ABSTRACT FROM AUTHOR]