This paper wants to investigate the effects of eco-friendly fluids on the thermo-fluid-dynamic performance of external gear pumps in order to provide a first response to the increasingly urgent demands of the green economy. A computational fluid dynamics (CFD) approach based on the overset mesh technique was developed for the simulation of the full 3D geometry of an industrial pump, including all the characteristic leakages between components. A sensibility analysis of the numerical model with respect to different fluid properties was performed on a commonly used mineral oil, showing the key role of the fluid compressibility on the prediction of the pump volumetric efficiency. Moreover, the influence of temperature internal variations on both fluid density and viscosity were included. The BIOHYDRAN TMP 46 eco-friendly industrial oil and olive oil were further considered in this work, and the results of the simulations were compared for the three fluid configurations. A slightly lower volumetric efficiency was derived for the olive oil application against the other two conditions, but suggestive improvements were produced in terms of pressure and temperature distributions. Therefore, based on the obtained results, this paper encourages research activity towards the use of eco-friendly fluids in the hydraulic field.