The prompt phase emission process of the Gamma-Ray Bursts (GRB) is still an open question. The GRB spectrum is often well fitted by an empirical smooth broken power-law function term as the Band model. However, observations from the Gamma-ray Burst Monitor (GBM) onboard the Fermi Gamma-Ray space telescope suggest the presence of a thermal component along with the non-thermal, whose origin is unintelligible. We perform a detailed study of the relativistically expanding fireball model with its temperature evolving with radius. The effect of the light travel time combined with the radially averaged spectrum results in a much broader spectrum compared to a Planck function. For this scenario, a numerical code was developed and coupled with the XSpec a local model. The time-averaged spectrum of the bright GRB 170409A was studied using the Fermi-GBM data. We find the spectrum is comprised of a thermal (multi-temperature black body model) and a non-thermal (cutoff power law) component. Our fit results suggest the emission is dominated by the thermal process with a photospheric radius of \(R_{ph} = 12.82_{0.07}^{-0.05}\) log cm, photospheric temperature \(T_{ph} = 1242.9_{141.5}^{-110.0}\) keV and bulk flow of the plasma \(\Gamma = 457.6_{142.5}^{-124.7}\) .