The constitutive formulation of the finite-strain thermoelasticity is revisited within the thermodynamic framework and the multiplicative decomposition of the deformation gradient into its elastic and thermal parts. An appealing structure of the Helmholtz free energy is proposed. The corresponding stress response and the entropy expressions are derived. The results are specified in the case of quadratic dependence of the elastic strain energy on the finite elastic strain. The specific and latent heats are discussed, and the comparison with the results of the classical thermoelasticity are given.