We describe a method for measuring heat capacity of small specimens in the 1.5–10 K range by means of thermal relaxation over that range. Our methods of calibration and analysis make use of the simple properties of the thermal link between specimen and its surroundings, and offer several advantages. The cryostat has been used in magnetic fields of up to 4.5 T, and simple relationships for the magnetoresistance of heat links and thermometer have been determined. Measurement of the heat capacity of a 90 mg copper sample shows that the method is accurate to 1%.