A contact system includes a support body, a heat sink configured to contact the support body in an electrically insulated and/or heat-conducting manner, and an electrically insulating layer arranged between the heat sink and the support body. The heat sink has a first surface which is embodied substantially as a flat area and formed with a recess in a region intended for contacting a periphery of a contact area of the support body. The recess forms an unbroken track on the first surface of the heat sink. The contact area of the support body is located on the heat sink in such a way that the recess extends completely along the periphery of the contact area. The insulating layer between the heat sink and the support body is configured to cover the recess in such a way that a closed channel is formed by the recess and the insulating layer.