The determination of the physical parameters of coronal loops remains both an observational and a theoretical challenge. A new diagnostic technique for quiescent dynamically heated coronal loops, based on the analysis of the power spectra of Doppler shift time series, is proposed. It is assumed that a given loop is heated randomly both in space and time by small-scale discrete impulsive events of unspecified nature. It is shown here that, depending on the heliographic position of the loop and the orientation of the observing instrument, various harmonics can be identified in the power spectra of line shift time series. The frequency peaks are sensitive to changes in the average loop temperature and are proposed to use as a temperature diagnostic tool. The analysis of the power spectra also allows to distinguish uniformly heated loops from loops heated near their footpoints.