The invention relates to a cooling device for a heat source, especially LED modules fitted with many components, said device comprising a base body (2) that is in thermal and mechanical contact with the body of the heat source (12), at least one thermoconducting tube (4, 5, 6) having an end section that is inserted into the base body (2) in a form-fitting and thermoconducting manner, and at least one cooling body (3) comprising cooling body lamellae (20) on the other end section of the thermoconducting tube. The invention is characterised in that the thermoconducting tubes (4, 5, 6) extend over the entire length of the base body (2) such that a hot zone (16, 34) of the heat source (12) lies on a contact surface (21) of the base body (2), the thermoconducting tubes extend parallel to each other and parallel to the contact surface of the heat source with the hottest zone (16, 34), and the base body (2) is fixed to the body of the heat source (12), base body lamellae (10) being provided on the outer side of the base body (2), formed as a single component thereon or connected thereto.