An AC calorimeter ranging from 4.2 to 400 K has been built and optimized in our laboratory for the study of solid-solid phase transitions. Only a small amount of sample is required (with typical dimensions of (2-6) mm x (2-4) mm x (0.2-0.5) mm and mass around 1-25 mg) and different types of solids such as insulator crystals or metal samples can be studied. Small-diameter thermocouples (25 mum) are used as temperature sensors and also as sample support. This system can be operated discontinuously with temperature jumps as small as 0.025 K or by continuous heating or cooling with scanning rates from 0.06 up to 6 K/min. Both procedures are governed by an automatic control program and data acquisition which provides very low dispersion of the C-p points (0.1%). The whole experimental set up was tested by new measurements of the triglycine sulphate (TGS) specific heat. Finally, the ferroelectric phase transition in the TGS is studied within the frame of the Landau theory. With this model, the specific heat is correctly described down to 15 degreesC below the transition temperature leading to accurate calculations of the phase transition thermodynamic functions.