A new differential flow heat capacity calorimeter was constructed. It is designed to operate at temperatures up to 700 K and pressures up to 35 MPa and its primary use is for determining the massic heat capacities at constant pressure of dilute aqueous solutions. The instrument works in the so-called isoperibol regime, where the fluid sample flowing through the cell is heated by an electrical heater and the power necessary to provide a constant temperature rise is measured relative to that for a reference fluid (water). From the two values of power for sample and water the ratio of massic heat capacities of the sample to that of water can be calculated. A thorough investigation of calibration techniques showed that the calorimetric performance is very sensitive to the thermal conductivities of the sample and reference fluids. Measurements under turbulent flow conditions are questionable since there is no guarantee that by changing the flow rate the experiments and the calibrations would be performed at the same flow conditions. The procedure is very accurate and sensitive when measuring the difference in heat capacity between a solvent and a dilute solution of solute in the same solvent. The calorimeter was used to measure heat capacities of aqueous solutions of NaCl at eight temperatures up to 623 K and pressures to 30 MPa. The newly obtained values show consistency with previously published results and enlarge the database of experimental values above T = 573 K, where experimental data are rare.