Summary: This article extends the previous authors’ paper [SIAM J. Math. Anal. 38, No. 6, 1733–1759 (2007; Zbl 1131.35083)] on the existence of solutions to a quasilinear thermoviscoelasticity system arising in shape memory alloy theory. In the present setup we admit a modified energy equation with temperature-growing specific heat. Due to such a modification, we can solve the problem with thermomechanical nonlinearity stronger as considered in the cited work.