The invention relates to a high voltage battery (1) for supplying power, in particularly of a motor vehicle, comprising an energy storage module (2) with several electrochemical storage cells (3) and a wall (6, 7) housing the plurality of storage cells (3), each storage cell (3) comprising at least two electric connection terminals (4, 5), and an upper part (8) for contacting and covering the connection terminal (4, 5), said upper part (8) overlapping the wall (6, 7) contactlessly such that a gap (11) remains to the storage cells (3).