The invention relates to a cooling body (1) for electrically insulating and / or thermally conducting contact with a support body (2), wherein the cooling body (1) has a first surface (10). In order to improve the contact, it is proposed that the first surface (10) has at least one recess (11), wherein the recess (11) is arranged in a region of the first surface (10) which is provided for edge contact with a contact surface (21) of the support body (2), wherein the recess (11) forms a
closed path on the first surface (10), wherein the first surface (10) is essentially configured as a planar surface. The invention also relates to a
contact system (3) having such a cooling body (1) and a support body (2), wherein the contact surface (21) of the support body (2) is arranged at the cooling body (1) such that the recess (11) of the cooling body (1) extends completely along the edge of the contact surface (21). The invention also relates to a method for producing such a
contact system (3), wherein the support body (2) is placed on the cooling body (1) such that the entire edge of the contact surface (21) of the support body (2) extends along the recess (11) of the cooling body (1).