We consider the finite-temperature dynamical suscepibility, X(T), of gapped quantum spin chains such as the integer spin Heisenberg model and the transverse field Ising model. At zero temperature X 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. We discuss the application of our results to inelastic neutron scattering experiments on gapped spin chain systems such as YBaNiO_5.