We investigated the thermodynamic processes of two-dimensional (2D) metallo-supramolecular self-assembly at molecular resolution using scanning tunneling microscopy and variable-temperature low-energy electron diffraction. On a Au(111) substrate, tripyridyl ligands coordinated with Cu in a twofold Cu-pyridyl binding mode or with Fe in a threefold Fe-pyridyl binding mode, forming a 2D open network structure in each case. The network structures exhibited remarkable thermal stability (600 K for the Cu-coordinated network and 680 K for the Fe-coordinated network). The Fe-pyridyl binding was selected thermodynamically as well as kinetically in self-assembly involving both modes. The selectivity can be effectively suppressed in a specifically designed self-assembly route.