Two-dimensional organic and metal-organic nanoporous networks can scatter surface electrons, leading to their partial localization. Such quantum states are related to intrinsic surface states of the substrate material. We further corroborate this relation by studying the thermally induced energy shifts of the electronic band stemming from coupled quantum states hosted in a metal-organic array formed by a perylene derivative on Cu(111). We observe by angle-resolved photoemission spectroscopy (ARPES), that both, the Shockley and the partially localized states, shift by the same amount to higher binding energies upon decreasing the sample temperature, providing evidence of their common origin. Our experimental approach and results further support the use of surface states for modelling these systems, which are expected to provide new insight into the physics concerning partially confined electronic states: scattering processes, potential barrier strengths, excited state lifetimes or the influence of guest molecules.