A three-dimensional approximate analytic solution is presented for the unequal countercurrent heat transfer between parallel paired vessels asymmetrically embedded in a long cylinder with surface convection. The analysis assumes that the velocity profile in the vessels is parabolic, the Peclet number is large compared to unity and the radius of the cylinder is several times larger than the distances from the center of the cylinder to the vessels. A perturbation method is employed by taking the reciprocal of the Peclet number as a small parameter. The new solution approach takes into consideration the axial thermal interaction and describes the three-dimensional asymmetric thermal field due to the vessels, the wall temperatures of which are nonuniform in the cross-sectional plane. Application of the model to whole limb heat transfer is discussed.