A semi-analytic method is used in order to systematically compute stationary 3-D coupled convection-diffusion in various parallel counter-current configurations and evaluate their thermal significance. This semi-analytic method permits a complete exploration of physiologically relevant parameter space associated with the bio-heat transfer of parallel vessels bundles. We analyze thermal significance with various previously proposed criteria. Optimal transfer configurations are found to depend on the vascular density and Péclet numbers. The relevance of these findings for bio-heat modeling in tissues is discussed.