A CFD-based numerical model has been developed for the determination of the volume concentration and number density of soot in a laminar diffusion flame of methane in air, under transient condition following ignition of the flame. The transience is studied from the point of ignition till the final steady state is reached. The burner is an axisymmetric co-flowing one with the fuel issuing through a central port and air through an annular port. Both normal air (non-preheated) and preheated air have been used for this simulation to capture the effect of preheating on soot distribution. Attention is focused on various soot forming and destruction processes, like nucleation, surface growth and oxidation, during the transient phase to evaluate their relative importance. The transient soot distribution has been studied with the help of radial distributions of soot at six different axial heights of 2 cm, 4 cm, 6 cm, 8 cm, 10 cm and 12 cm respectively above the burner tip. Beyond 12 cm height, the concentration becomes very less in all cases. The contribution of surface growth towards soot formation is more significant than that of nucleation during the early periods following ignition. Once the high temperature reaches the oxygen-enriched zone beyond the flame, the soot oxidation becomes important. Coagulation, on the other hand, limits the soot particle number. Preheating of air increases the soot volume fraction in the flame significantly. But, the soot distribution patterns remain almost similar to that with non-preheated air during the flame transient period and also in the steady state.