A battery system (2) for use in an Electric Vehicle (1), EV, is provided. The battery system (2) comprises a battery cell (20, 30, 40), a conductor (14, 15, 28; 35a, 35b) comprising graphene, and a cooling member (16), wherein the battery cell is in thermally conductive connection to the cooling member (16) via the conductor (14, 15, 28; 35a, 35b). The disclosure further relates to a battery cell for use in the battery system and to a vehicle (1) comprising the battery system.