The finite-temperature effect of a quantized conformally invariant scalar field in a closed Robertson-Walker universe is studied. The general solution is characterized by one parameter ξ = Ta which measures the radiation content of the universe. In the high-temperature limit it reduces to the Fischetti-Hurtle-Hu solution where the universe expands linearly in cosmic time near the singularity. In the low-temperature limit, it reduces to a Starobinsky-de Sitter type solution where the singularity is avoided in an exponential expansion. Several characteristic functional dependences of ξ(t) are used to illustrate possible entropy generating processes. The finite-temperature formalism thus provides a unifying framework for the description of the interplay of vacuum and radiation energy and their combined effect on the state of the early universe.