DRAMs or dynamic semiconductor memories comprise a multiplicity of memory cells in order to store information. The memory cells of a DRAM can retain their information only for a specific time. For this reason, a refresh must be carried out at specific time intervals. Devices for generating a refresh signal for a memory cell of a semiconductor memory device are known which periodically generate a refresh signal and output it to the memory cell. However, these devices have the disadvantage that the refresh frequency or refresh period is the same for all operating temperatures of the semiconductor memory device, and, consequently, in particular at low temperatures, for which a lower refresh frequency suffices, a refresh signal is output more often than necessary and, consequently, current is consumed unnecessarily by the semiconductor memory device.