This paper proves that any initial condition in the energy space for the system of thermoelastic plates without rotatory inertia on a smooth bounded domain with hinged mechanical boundary conditions and Dirichlet thermal boundary condition can be steered to zero by a square integrable input function, either mechanical or thermal, supported in arbitrarily small sub-domain and time interval [0,T]. As T tends to zero, for initial states with unit energy norm, the norm of this input function grows at most like exp( C_p / T^p ) for any real p > 1 and some C_p > 0. These results are analogous to the optimal ones known for the heat flow and the proof uses the heat control strategy of Lebeau and Robbiano.