The AC temperature technique is used to develop a calorimeter probe for measuring the specific heat of small samples. A commercial closed-cycle refrigerator operating in the 8 - 300 K temperature range was used as a cryogenic station. A theory of operation is presented and the experimental set-up is discussed. The calorimeter has been used to study the nature of the magnetic and order - disorder phase transitions of several materials. Specific heat data taken from a sample of chromel alloy (90% Ni - 10% Cr) and a single-crystal sample of show that the sensitivity of the apparatus to relative variations in the specific heat is about 0.1%.