The paper deals with the generalized thermoelasticity variational problem: for a given \(u_0\in V, \nu_0\in H, \theta_0\in Z, q_0\in R, (l,\mu)\in L^{2}(0,T;V'\times G')\) find a triple \(\psi=(u,\theta,q)\in L^2(0,T;V\times G\times R)\) such that \[ \begin{cases} m(u''(t),\nu)+a(u'(t),\nu)+c(u(t),\nu)-b(\theta(t),\nu)=\rangle l(t),\nu\langle;\\ s(\theta'(t),\xi)+d(q(t),\xi)+b(\xi,u'(t))=\rangle\mu(t),\xi\langle;\cr \tau_{r}k(q'(t),r)-d(r,\theta(t))+k(q(t),r)=0;\\ m(u'(0)-\nu_0,\nu)=0,\;c(u(0)-u_0,\nu)=0,\;\forall \nu\in V;\cr s(\theta(0)-\theta_0,\xi)=0,\;k(q(0)-q_0, r)=0,\;\forall\xi\in G, \forall r\in R. \end{cases} \] Here \(\tau_{r}\geq 0\) is a coefficient of thermal relaxation. Using the Galerkin semidigitization on spatial variables and energy equation the authors prove the existence and unique theorem for the given variational problem.