A series of true stress-strain curves measured in tension, published by Hiss and Strobl [Deformation, yield and fracture of polymers (1997) 439], have been modelled using a Gaussian equation to represent strain hardening. An empirically-based constitutive relation was extracted from the data spanning the temperature range 24-128 degreesC, In the first procedure, adiabatic heating was introduced into the constitutive relation at constant true strain rate by means of an explicit integration scheme that equates incremental plastic work to a temperature rise. At the end of each increment the material proper-ties were adjusted to account for the increase in temperature, In the second procedure, a constant load was assumed and the temperature rise was calculated directly from the work done together with a curve relating temperature to energy input. In each case, it was found that adiabatic conditions had a destabilising effect, which was interpreted using the Vincent-Considere criteria. The possibility of using draw stress instead of yield stress in the calculations was considered and it was concluded that such a change would not qualitatively affect the results. The rise in deformation stresses and the reduction in specific heat at low initial temperatures is expected to increase the thermomechanical instability. These conclusions were shown to be insensitive to minor changes in crystallinity during deformation.