The dynamics of a viscous film flowing down a vertical fibre under the action of gravity and the thermocapillarity induced by an axial temperature gradient is investigated theoretically. The instability of this exterior coating flow is driven by a Rayleigh-Plateau mechanism modified by the presence of gravity as well as the thermocapillarity. We derived an evolution equation for the interface in the framework of the long wave approximation. A linear stability analysis and a nonlinear simulation are performed to investigate the influence of the thermocapillarity on the dynamics of axisymmetric disturbances. The results of linear stability showed that the thermocapillarity does not influence the growth rate of the disturbance and only affects its frequency. For the nonlinear evolution, the thermocapillarity plays an important role in influencing the profile of the interface in different flow regimes. We also examined the effect of thermocapillarity on the wave speed and the characteristics of the structures of travelling wave solutions. Crown Copyright (C) 2018 Published by Elsevier Ltd. All rights reserved.