The structural, electronic and magnetic properties of two different models of the heterospin polymer chain complexes of Cu2+ hexafluoroacetylacetonate with two pyrazole-substituted nitronyl nitroxides Cu(hfac)2L(R) have been studied by means of multiconfigurational perturbation theory based on a CASSCF (complete active space self-consistent field) wave function, i.e. the CASPT2 method. Our calculations reveal the presence of two minima in the electronic energy curve along the Cu-O(L) bond, separated by only 6 kcal/mol, and corresponding to the X-ray structures of the CuO6 centers in Cu(hfac)2L(Pr) at 115 and 293 K, respectively. The two energetic minima are characterized by a different electronic structure, thus giving rise to a different three-spin exchange coupling and explaining the thermally induced spin transitions in this family of compounds. The concomitant variations in the magnetic properties, i.e. g factors and magnetic moments mu(eff)(T) were calculated and compared with the experimental data of Cu(hfac)2L(Pr). Even if the correspondence is only qualitative, our calculations provide a convincing explanation of the observed magnetic peculiarities. In particular, at low temperatures, the predicted ground-state is 2A(u), well separated from the 2A(g), 4A(u) states and therefore exclusively populated. Its calculated g factors, g(parallel) = 1.848, g(perpendicular) = 1.965, 1.974, qualitatively correspond to the observed g < 2 signals in the low-temperature EPR spectra. The previously assumed formal spin assignment >N-O*-Cu-*O-N < for these linear spin triads is challenged by our calculations, pointing instead to a more important role of the end-standing NO in the exchange interactions with Cu(II).