A commercially available calorimeter has been used to investigate the specific heat of a high-quality K_0.71Na_0.29Fe₂As₂single crystal.The addenda heat capacity of the calorimeter is determined in the temperature range 0.02K ≤ T ≤ 0.54K. The
data of the K_0.71Na_0.29Fe₂As₂ crystal imply the presence of a large T² contribution to the specific heat which gives evidence of d-wave order parameter symmetry in the superconducting state. To improve the measurements, a novel design for a calorimeter
with a paramagnetic temperature sensor is presented. It promises a temperature resolution of ΔT ≈ 0.1μK and an addenda heat capacity less than 200 pJ/K at T < 100mK.