An LED illumination module is described, where a row of LED elements (1) is arranged via a substrate (16) on a secondary cooling element (2). The secondary cooling element (2) can consist of a first material layer (16, 17) of copper and a second material layer (18) of aluminium. In such material combinations, phononic refraction leads to a good lateral heat distribution, which improves the heat flow and reduces temperature gradients. Alternatively or in addition thereto, the secondary cooling element (2) can be equipped with heat pipes. The LED elements (1) are electrically contacted by means of a current supply member (21) arranged at a distance from the substrate (16).