We describe the construction, operation and performance O f a fully automated low temperature differential micro-calorimeter for heat capacity measurements on small samples (m < 100 rag) in the temperature range from 15 K to 300 K. The instrument is operated using different calorimetric methods, in particular adiabatic differential scanning. Its reliability is demonstrated by measuring the heat capacity of 23 mg of copper and 37 mg of cyclopentane with an error of less than 2%.