Rapid cycling solutions are presented for a simple two-bar structure subjected to variable temperature. Three constitutive relationships are considered, nonlinear viscous, strain-hardening and Bailey-Orowan models which describe differing aspects of the creep of metals. It is shown that the solutions for the viscous and strain-hardening relations are essentially similar and possess distinct reference stress histories over ranges of the governing parameters. The presence of recovery in the Bailey-Orowan model causes a distinctly different mode of behavior. Experimental results on a simulated two-bar structure are presented, under conditions where the strain-hardening hypothesis may be expected to be most relevant. Good agreement is obtained between theory and experiment although the presence of anelastic creep, with a short time scale, tends to reduce the effective thermoelastic stresses.