Unique continuation of solutions to linear partial differential equations is of importance in many branches of applied mathematics, in particular, in control theory and inverse problems. The Carleman estimates are an important tool for proving the unique continuation for linear operators with non-analytic coefficients. In this paper, the author combines the approaches by \textit{D. Tataru} [Commun. Partial Differ. Equations 20, No.~5-6, 855-884 (1995; Zbl 0846.35021)] and \textit{V. Isakov} [Preprint, 1998] to obtain a new Carleman estimate with two large parameters for operators with time independent coefficients. This estimate is the foundation of the local uniqueness result for the thermoelastic system: \(w_{tt}-\gamma \Delta w_{tt} +\Delta^2 w +\operatorname {div} (\alpha (x) \nabla \theta)=0\),\quad \(\theta_t -\Delta\theta -\operatorname {div} (\alpha (x) \nabla w_t)=0\).