Absorption spectra of I-2 dissolved in n-heptane and CCl4 are analyzed with a quantum gas phase model, in which spectra at four temperatures between 15 degrees and 50 degrees C are least-squares fitted by bound-free spectral simulations to obtain estimates of the excited-state potential energy curves and transition moment functions for the three component bands-A <- X, B <- X, and C <- X: Compared with a phenomenological band-fitting model used previously on these spectra, the physical model (1) is better statistically, and (2) yields component bands with less variability. The results support the earlier tentative conclusion that most of the similar to 20% gain in intensity in solution is attributable to the C <- X transition. The T-dependent changes in the spectrum are accounted for by potential energy shifts that are linear in T and negative (giving red shifts in the spectra) and about twice as large for CCl4 as for heptane. The derived upper potentials resemble those in the gas phase, with one major exception: In the statistically best convergence mode, the A potential is much lower and steeper, with a strongly varying transition moment function. This observation leads to the realization that two markedly different potential curves can give nearly identical absorption spectra.