Abstract Two stabilized implicit-implicit numerical solution techniques for solving strong, two-way coupled, linear, thermomechanics are compared. The first technique is a semi-algebraic, augmented procedure originally developed by Farhat et al. [An unconditionally stable staggered algorithm for transient finite element analysis of coupled thermoelastic problems. Computer Methods in Applied Mechanics and Engineering 1990]. The second solution technique is a time-stepping numerical solution based upon a staggered predictor method similar to that of Zienkiewicz et al. [Unconditionally stable staggered solution procedure for soil-pore fluid interaction problems. International Journal for Numerical Methods in Engineering, 1988, 26, 1039–1055]. First, the motivation for solving coupled systems using staggered finite element techniques is presented. Next, the development of the numerical stabilization for the two implicit-implicit staggered algorithms is discussed. This is then followed by a comparison of numerical stability, consistency and efficiency for a specific class of thermoelastic problems. Finally, conclusions are drawn as to the effectiveness of solving parabolic/hyperbolic coupled systems using stabilized implicit-implicit staggered procedures.