<p>Almost all the properties of cuprate high-temperature superconductors are no less mysterious than their superconductivity. From the very beginning of their study, it was noted that a two-component system of charge carriers is suitable for their description, which, however, had to be introduced phenomenologically. Recently it has been shown that ground and low-excited states of a system with strong long-range electron-phonon interaction and cuprates-like dispersion at carrier densities characteristic of cuprate superconductors are a two-liquid system of charge carriers comprising Bose-liquid of large bipolarons and Fermi-liquid of delocalized carriers. The phase diagram of such a system was demonstrated to coincide with that observed in cuprates. The temperature of the superconducting transition in them was shown to increase with the number of conducting layers in the unit cell, like in cuprates, due to the change in the spectrum of elementary excitations of the bipolaron liquid. Here we calculate temperature and doping behavior of the electronic specific heat and Hall resistance of such systems and compare it with that observed in cuprates. The low-temperature electronic specific heat obtained demonstrates giant increase at increasing doping, like that observed in cuprates at the overdoping. The increase is related with gradual decay of bipolarons at increasing temperature or doping. We also show that this decay may be responsible for the decrease in Hall resistance with increasing temperature observed in cuprates.</p>