A sealing device for sealing a lid material to sealing areas of a blister web comprises a first, heated sealing tool and a second sealing tool arranged opposite each other and movable relative to each other. A first intermediate element of elastic material is attached to the first sealing tool on a side facing the second sealing tool, and a second intermediate element of thermally-insulating material is attached to the second sealing tool on a side facing the first sealing tool. The first and second sealing tools are movable relative to each other between an opened position and a closed position, in which at least sections of the first intermediate element and of the second intermediate element exert pressure on each other. In the closed sealing position, the first intermediate element rests on the lid material and the second intermediate element rests on lands of the blister web.