  We consider the finite-temperature dynamical structure factor (DSF) of gapped
quantum spin chains such as the spin one Heisenberg model and the transverse
field Ising model in the disordered phase. At zero temperature the DSF in these
models is dominated by a delta-function line arising from the coherent
propagation of single particle modes. Using methods of integrable quantum field
theory we determine the evolution of the lineshape at low temperatures. We show
that the line shape is in general asymmetric in energy and becomes Lorentzian
only at temperatures far below the gap. We discuss the relevance of our results
for the analysis of inelastic neutron scattering experiments on gapped spin
chain systems such as CsNiCl_3 and YBaNiO_5.
