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α-RuCl₃ is a promising Kitaev spin liquid candidate, but orders magnetically, the description of which necessitates additional interaction terms. The nature of these interactions, their magnitudes and even signs, remain an open question. In this work we investigate dynamical and thermal magnetic properties of proposed effective Hamiltonians. We calculate T=0 inelastic neutron scattering (INS) intensities using exact diagonalization, and magnetic specific heat, C(T), using a thermal pure quantum states method. We find that no single current model satisfactorily explains all observed phenomena of α-RuCl₃. In particular, we find that Hamiltonians derived from first principles can capture the experimentally observed high-temperature peak in C(T), while overestimating the magnon energy at q=0. In contrast, other models reproduce important features of the INS data, but do not adequately describe C(T). We propose a modified ab initio model that is consistent with both magnetic specific heat and low-energy features of INS data.