The thermal-hydraulic model of an electro-hydrostatic module involving a variable speed, fixed-displacement, internal-drain vane pump is developed at system level for analysis and for support of preliminary sizing. A generic model structure is proposed for the pump energy losses that are made dependent on velocity, pressure and temperature. Leakage and friction models are implemented accordingly. Model structure and implementation are proposed giving preference to re-using standard submodels of the AMESim software library and to balance model complexity and realism. Then, the proposed approach is deployed for simulating the temperature rise during static injection in moulding machines that are powered and controlled via an electro-hydrostatic module. In this particular phase, the pump operates at extremely low delivery flow, inducing a rapid temperature rise that may directly impact service life. For validation, a very penalizing approach is used which runs the model in open loop in response to motor electromagnetic torque, ambient temperature and hydraulic load resistance. Conclusions are drawn concerning the model accuracy and the mains issues encountered, regarding model structure, knowledge models and parameters preliminary determination.