Magnetic interactions in hybrid materials are poorly understood compared to those in purely inorganic materials. The high flexibility of many metal-organic systems introduces a strong temperature dependence of the magnetic exchange interactions owing to changes in the crystal structure. Here, we study the cobalt adipate system, for which anisotropic thermal expansion was recently shown to be a result of magnetoelastic coupling. The combination of density functional theory with quasi-harmonic lattice dynamics is shown to be a powerful tool for describing temperature dependent thermodynamic potentials that determine magnetic interactions. It is demonstrated that the effect of phonons can be sufficient to switch the preference for ferromagnetic versus antiferromagnetic ordering.