  We report on time-resolved spectroscopy of the 63 brightest bursts of SGR
J1550-5418, detected with Fermi/Gamma-ray Burst Monitor during its 2008-2009
intense bursting episode. We performed spectral analysis down to 4 ms
time-scales, to characterize the spectral evolution of the bursts. Using a
Comptonized model, we find that the peak energy, E_peak, anti-correlates with
flux, while the low-energy photon index remains constant at -0.8 up to a flux
limit F~10^-5 erg s-1 cm-2. Above this flux value the E_peak-flux correlation
changes sign, and the index positively correlates with flux reaching 1 at the
highest fluxes. Using a two black-body model, we find that the areas and fluxes
of the two emitting regions correlate positively. Further, we study here for
the first time, the evolution of the temperatures and areas as a function of
flux. We find that the area-kT relation follows lines of constant luminosity at
the lowest fluxes, R^2 \propto kT^-4, with a break at higher fluxes ($F>10^-5.5
erg s-1 cm-2). The area of the high-kT component increases with flux while its
temperature decreases, which we interpret as due to an adiabatic cooling
process. The area of the low-kT component, on the other hand, appears to
saturate at the highest fluxes, towards R_max~30 km. Assuming that crust quakes
are responsible for SGR bursts and considering R_max as the maximum radius of
the emitting photon-pair plasma fireball, we relate this saturation radius to a
minimum excitation radius of the magnetosphere, and put a lower limit on the
internal magnetic field of SGR J1550-5418, B_int>~4.5x10^15 G.
