An electrically heatable honeycomb body is formed with at least one wound stack of sheet-metal foils. A first end of the stack is connected to an electrical terminal and a second end is connected to an electrical ground. The stack has a plurality of sheet-metal foils which are in electrical contact with one another and which are at least partially structured and determine, in the direction of the structures, a height of the stack. The stack has at least one curvature with a small radius of curvature and a relatively large radius of curvature. A curvature section including the at least one curvature has at least one zone with increased electrical resistance starting from the small radius of curvature and extending over part of the height of the stack. A motor vehicle having at least one honeycomb body, is also provided.