Thermo-hydrodynamic lubrication of a polymeric liquid composed of short chains between parallel plates is analysed by a multi-scale simulation, i.e. the synchronised molecular dynamics simulation via macroscopic heat and momentum transfer, which has been recently developed by us. The rheological properties and conformation of polymer chains coupled with the temperature rise caused by local viscous heating are investigated with a non-dimensional parameter, i.e. the Nahme-Griffith number, which is defined by the ratio of the viscous heating to the thermal conduction at the characteristic temperature required to sufficiently change the viscosity. The present simulation demonstrates that strong shear thinning and transitional behaviour of the conformation of the polymer chains occurs with a rapid temperature rise when the Nahme-Griffith number exceeds unity.