Abstract: A mobile, in particular portable, energy supply system having battery modules which can be connected in series in a controllable manner in order to provide different voltages at a power supply connection of the energy supply system, and a control unit for controlling the battery modules, wherein each battery module has an input connection and an output connection, a battery unit for providing a module voltage and switching elements, in particular power electronic ones. The switching elements are designed to selectively switch the module voltage for the provision of energy to the input and output connection, wherein a heat-transferring coupling between the switching elements and the battery unit is provided to transfer operationally generated heat loss of the switching elements specifically from these to the battery unit. A battery module for an energy supply system and a method for operating such an energy supply system are also related.