A nonlinear model of thermoelasticity is solved for a ring-shaped body with special attention given to the effect of relaxation time on the body dynamics. A spectral Galerkin method is used to accurately resolve spatial structures of temperature and displacement. A sequence of solutions is obtained for gradually increasing initial amplitude of the thermoelastic wave, showing a transition from a steady harmonic wave to singular solutions. Larger values of the relaxation time are shown to result in smoother temperature profiles. The dynamics generated by a localised heat release from an external source is studied. It is observed that the source excites a standing-like wave of the displacement while temperature monotonically decays.