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Being directly observed in the Doppler shift and imaging data and indirectly as quasi-periodic pulsations in solar and stellar flares, slow magnetoacoustic waves offer an important seismological tool for probing many vital parameters of the coronal plasma. A recently understood active nature of the solar corona for magnetoacoustic waves, manifested through the phenomenon of wave-induced thermal misbalance, led to the identification of new natural mechanisms for the interpretation of observed properties of waves. A frequency-dependent damping of slow waves in various coronal plasma structures remains an open question, as traditional wave damping theories fail to match observations. We demonstrate that accounting for the back-reaction caused by thermal misbalance on the wave dynamics leads to a modification of the relationship between the damping time and oscillation period of standing slow waves, prescribed by the linear theory. The modified relationship is not of a power-law form and has the equilibrium plasma conditions and properties of the coronal heating/cooling processes as free parameters. It is shown to readily explain the observed scaling of the damping time with period of standing slow waves in hot coronal loops. Functional forms of the unknown coronal heating process, consistent with the observed frequency-dependent damping, are seismologically revealed.