NOVELTY - The battery system (10) includes prismatic battery cells consist of upper battery cell and lower battery cell with positive terminal (18P) and negative terminal (18N) which are arranged longitudinally along the longitudinal axis (L). A heat exchange passageway or conduit (98,102) is provided across the electrical connector that electrically couples positive and negative terminals of the cells. The heat exchange passageway is oriented parallel to the longitudinal axis, and is oriented transverse or perpendicular to the cells.    USE - Battery system used in hybrid vehicle or electric vehicle e.g. a car, bus as power source. Can also be used to store and provide energy to other devices which receive power from batteries such as the stationary energy storage market including providing power to power grid as uninterrupted power supply and other loads as stationary power source, and as uninterrupted power supply for computing devices and other equipment in data centers.    ADVANTAGE - Improves cooling of battery by providing it with heat exchange passageway as direct thermal path through which heat exchange medium passes across the electrical connector to cool the upper and lower cells, and by providing the electrical connector with heat transfer features that promotes cooling of the battery system. Separator is provided with fins which prevent contact between fins of adjacent electrical connectors to avoid electrical shorts, and conduits which communicate with conduits of adjacent electrical connectors to facilitate passage of the heat exchange medium in various direction. Temperature sensors e.g. thermistors are provided throughout the battery system to control the flow of the heat exchange medium and to regulate the cooling of battery system.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for an assembly method for battery system.    DESCRIPTION OF DRAWING(S) - The drawing shows the perspective view of the battery system with battery sub-assemblies.    Battery system (10)    Negative terminal (18N)    Positive terminal (18P)    Heat exchange passageway or conduit (98,102)    Longitudinal axis (L)