Using ferromagnetic-resonance spectroscopy (FMR), we investigate the anisotropic properties of epitaxial 3 nmPt/2 nmAg/10 nmFe/10 nmAg/GaAs(001) films in fully saturated meta-stable states at temperatures ranging from 70 K to 280 K. By comparison to spin-wave theory calculations, we identify the role of thermal fluctuation of magnons in overcoming the energy barrier associated with these meta-stable states. We show that the energy associated with the size of the barrier that bounds the meta-stable regime is proportional to the heat stored in the magnonic bath. Our findings offer the possibility to measure the magnonic contribution to the heat capacity by FMR, independent of other contributions at temperatures ranging from 0 K to ambient temperature and above. The only requirement being that the selected sample exhibits magnetic anisotropy, here, magnetocrystalline anisotropy.