When some faults take place in a thermal storage HVAC system, changing pattern of the temperature profiles of the thermal storage tank is useful to infer where some faults exist. Authors designed some parameters calculated from the temperature profiles of the thermal storage tank in HVAC system and their Fourier Transform to detect the difference between the normal and faulty state. Further, present paper shows practicality of two methods of parameter optimization, a differentiation rate increment method and a variable selection method, with an actual application to a hospital.