A thermo-mechanical model of a splash lubricated one-stage gear unit is presented. This system corresponds to a first step towards the design of a hybrid vehicle gearbox that can operate up to 40,000 rpm on its primary shaft. The numerical model is based on the thermal network method and takes into account power losses due to teeth friction, rolling-elements bearings and oil churning. Some calculations underline that oil churning causes a high amount of power loss. A simple method to reduce this source of power losses is presented, and its influence on the gear unit efficiency and its thermal capacity is computed.