A class of models describing the evolution of the homogeneous and isotropic spatially flat Universe filled with a scalar field and matter and changing the equation of state during its evolution from a vacuum-like form to an ideal liquid is proposed under the assumption that both components of matter are in thermal equilibrium. The main characteristics of such models are analyzed and their asymptotic behavior in the vicinity of a cosmological singularity and at the postinflation stage is investigated. It is shown that the thermal equilibrium condition and the requirement of asymptotic decrease of the field with time unambiguously lead to secondary inflation at the final stage of evolution, which is accompanied by accelerated expansion of the Universe and an increase in the temperature of matter.
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