A new wavelet analysis method is used to study heat pulse propagation in magnetic confinement plasmas. The wavelet transform is applied to estimate the time evolution of the phase delay in heat pulse propagation with a fine temporal resolution. The procedure of analysis is explained in detail. The method is examined by taking an exemplary heat pulse propagation in the Large Helical Device. Various wavelet parameters are tested and the parameter region where relevant results are obtained is identified. Temporal resolution of the phase variation is evaluated from a convergence study.