Gamma-ray bursts (GRB) are extremely energetic events and produce highly diverse light curves. Light curves are believed to be resulting from internal shocks reflecting the activities of the GRB central engine. Hence their temporal studies can potentially lead to the understanding of the GRB central engine and its evolution. The light curve variability time scale is an interesting parameter which most models attribute to a physical origin e.g., central engine activity, clumpy circum-burst medium, or relativistic turbulence. We develop a statistical method to estimate the GRB minimum variability time scale (MVT) for long and short GRBs detected by GBM. We find that the MVT of short bursts is distinctly shorter than that for long GRBs supporting the possibility of a more compact central engine of the former. We find that MVT estimated by this method is consistent with the shortest rise time of the fitted pulses. Hence we use the fitted pulse rise times to study the evolution of burst variability time scale. Variability time is in turn related to the minimum bulk Lorentz factor. Using this we relate the GRB spectral evolution to the evolution of the variability time scale.