Summary: This paper develops an abstract framework for analysis and approximation of linear thermoelastic control systems, and for design of finite- dimensional compensators. The thermoelastic systems in this paper consist of abstract wave and diffusion equations coupled in a skew self-adjoint fashion. Linear semigroup theory is used to establish that the abstract thermoelastic models are well posed and to prove convergence of generic approximation schemes. Open-loop uniform exponential stability for a subclass of thermoelastic systems is proved via a Lyapunov function. An example involving the design of an optimal linear-quadratic-Gaussian (LQG) compensator for a thermoelastic rod illustrates the application of the abstract theory. Results of an extensive numerical study, including a comparison of the closed-loop performance of different compensator designs, are presented and discussed.