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Non-equilibrium molecular dynamics simulations have expanded our ability to investigate interfacial thermal transport and quantify the interfacial thermal conductance (ITC) across solid and fluid interfaces. NEMD studies have highlighted the importance of interfacial degrees of freedom and the need to include effects beyond traditional theoretical methods that rely on bulk properties. NEMD simulations often use explicit hot and cold thermostats to set up thermal gradients. We analyse here the impact of the thermostat on the calculated ITC of the gold-water interface. We employ a polarisable model for gold based on Drude oscillators. We show that the 'local' Langevin thermostat modifies the vibrational density of states of the polarisable solid, resulting in ITCs that depend very strongly on the damping constant of the thermostat. We report an increase of the ITC of up to 40% for short damping times. Damping times longer than the characteristic heat flux relaxation time of the solid lead to converging ITCs. In contrast, the ITCs obtained with global canonical velocity rescale thermostats are independent of the damping time but lead to a break of equipartition for Drude particles. Setting individual thermostats for the core and shell sites in the Drude particle solves this problem. [ABSTRACT FROM AUTHOR]