We present the results of our broadband (0.5 − 200 keV) spectral analysis of 42 SGR J1550–5418 bursts simultaneously detected with the Swift/X-ray Telescope (XRT) and the Fermi/Gamma-ray Burst Monitor (GBM), during the 2009 January active episode of the source. We find that, on average, the burst spectra are better described with two blackbody functions than with the Comptonized model. Thus, our joint XRT/GBM analysis clearly shows for the first time that the SGR J1550–5418 burst spectra might naturally be expected to exhibit a more truly thermalized character, such as a two-blackbody or even a multi-blackbody signal. We also studied the spin phase of the XRT burst emission, which indicate that the burst emitting sites on the neutron star need not to be co-located with hot spots emitting the bulk of the persistent X-ray emission and the surface magnetic field of SGR J1550–5418 is likely non-uniform over the emission zone.