Intrinsic temperature oscillations (with the amplitude up to 1 K) of a closed cycle cryocooler are stabilized by a simple thermal damping system. It employs three different materials with different thermal conductivity and specific heat at various temperatures. The amplitude of oscillations of the sample temperature is reduced to less than 1 mK, in the temperature range from 4 K to 300 K, while the cooling power is virtually undiminished. The damping system is small, inexpensive, can be retrofitted to most existing closed cycle cryocoolers, and may improve measurements of any temperature-sensitive physics properties. (C) 2014 AIP Publishing LLC.