The temperature field in the coupled, dynamic theory of linear thermoelasticity for homogeneous and isotropic bodies satisfies a partial differential equation in which the temperature is the only unknown-the so-called temperature equation. Here, for certain classes of problems, appropriate boundary and initial conditions are derived for the temperature equation from the data for the corresponding mixed problem of thermoelasticity. It is shown that the resulting boundary-initial-value problem for the temperature has at most one solution. Furthermore, for these classes of problems, it is shown that a displacement field can be ex pressed directly in terms of the temperature field and that the corresponding thermoelastic process satisfies all of the conditions of the mixed thermoelasticity problem except for the tangential components of the mechanical boundary conditions. To this extent, our boundary-initial-value problem for the temperature uncouples the coupled theory.