The mechanism of the thermomechanical instability of an elastically slowly strained solid is explored, by a normal mode analysis of temperature and strain fluctuations. The strain dependence of the Gruneisen parameter is found to play a major role, since it controls the rates of damping of the lowest wavevector acoustic excitations pumped by the imposed strain. For α-titanium the instability is found to occur at a critical strain comparable with that of the elastic limit. The instability can be envisaged in terms of a fast growing deformation, presumably associated with an acoustic emission.