In this paper, the author considers a general control problem about the system of thermoelasticity of type I. By introducing some unique continuation property of the corresponding adjoint system and a suitable observability inequality for an elastic equation, using compact decoupling technique and variational approach, the exact-approximate controllability of the abstract thermoelasticity of type I is obtained. Finally, the author applies her abstract result to the exact-approximate controllability of the linear system of thermoelasticity.