Global volcanic and tectonic activity observed on medium size icy satellites (MIS) of Saturn are probably a result of solid-state convection driven by tidal and radiogenic heating. A parameterized model of such convection is developed and applied for MIS. We find that some satellites could be in one of a few possible thermal states (basic or excited). It could explain the Mimas–Enceladus paradox. We use also the model and some elementary constrains to estimate the rate of tidal heat production qtid, internal temperature, the Rayleigh number and some material parameters of the MIS’s interiors. We find that for Enceladus qtid is 10 times (or more) higher than the rate of radiogenic heating qrad. This estimation is confirmed recently by Cassini. For dead satellites qtid is lower or comparable to the rate of radiogenic heating qrad. The past endogenic activity of Dione may be a result of higher eccentricity of its orbit or of being in an excited state. The basic thermal properties of MIS are described by our uniform model, so MIS seems be rather a homogenous group.