We present the continuation of our long-term spectroscopic monitoring of the gravitationally lensed quasar QSO 2237 + 0305. We investigate the chromatic variations observed in the UV/optical continuum of both quasar images A and B, and compare them with numerical simulations to infer the energy profile of the quasar accretion disk. Our procedure combines the microlensing ray-shooting technique with Bayesian analysis, and derives probability distributions for the source sizes as a function of wavelength. We find that the effective caustic crossing timescale is 4.0 +/- 1.0 months. Using a robust prior on the effective transverse velocity, we find that the source responsible for the UV/optical continuum has an energy profile well reproduced by a power-law R proportional to lambda(zeta) with zeta = 1.2 +/- 0.3, where R is the source size responsible for the emission at wavelength.. This is the first accurate, model-independent determination of the energy profile of a quasar accretion disk on such small scales.