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The light curves of gamma-ray bursts (GRBs) are believed to result from internal shocks reflecting the activity of the GRB central engine. Their temporal deconvolution can reveal potential differences in the properties of the central engines in the two populations of GRBs which are believed to originate from the deaths of massive stars (long) and from mergers of compact objects (short). We present here the results of the temporal analysis of 42 GRBs detected with the Gamma-ray Burst Monitor onboard the Fermi Gamma-ray Space Telescope. We deconvolved the profiles into pulses, which we fit with lognormal functions. The distributions of the pulse shape parameters and intervals between neighboring pulses are distinct for both burst types and also fit with lognormal functions. We have studied the evolution of these parameters in different energy bands and found that they differ between long and short bursts. We discuss the implications of the differences in the temporal properties of long and short bursts within the framework of the internal shock model for GRB prompt emission.