A formulation of the unit cell model and the corresponding thermal performance analysis for the cross-flow heat exchanger are carried out, with the design goal of dissipating 175 W from a high-power electronic chip in a compact space. A liquid to liquid heat exchanger in the cross-flow arrangement is preferred due to its compact size and high effectiveness. The unit cell model is formulated based on the volume-averaging method to determine the heat transfer coefficient involving two heat exchanging fluids and a solid. The various factors such as channel shape, channel edge length, channel size, and heat exchanger material can be examined based on the unit cell model. The obtained heat transfer coefficients are used for the estimation of the heat exchanger thermal performance based on the effectiveness–number of transfer units (NTU) correlation. To verify the model formulation, the heat and fluid flow over the cross-flow heat exchangers are investigated through the full-field numerical computation. The amount of heat exchanged from the numerical computation is extracted and compared with the predicted results from the unit cell model. A fairly good agreement is obtained between the two approaches. Based on the unit cell model, an aluminum cross heat exchanger with eight channel layers for the hot and cold fluids, 15 channels in each layer with a channel diameter of 2 mm, is able to meet the design target.