Known rechargeable batteries contain a cell that is received in a cell cup. For monitoring the temperature of the rechargeable batteries, PTC elements are used, but they increase the amount of space needed and can be accommodated in a battery pack only with difficulty. For the sake of simple accommodation, a rechargeable battery has a cell, which is received in a cell cup. According to the invention, for monitoring the temperature of the cell, a temperature-dependent element, in particular a PTC element, is provided that at least partially surrounds the cell cup. The invention is intended in particular for battery packs in which temperature monitoring is required.