Multicolor (BVRI) light curves of the eclipsing classical nova V Per are presented, and a total of twelve new eclipse timings have been measured for the system. When combined with previous eclipse timings from the literature, these timings yield a revised ephemeris for the times of mid-eclipse given by HJD = 2,447,442.8620(1) + 0.107123474(3) E. The eclipse profiles have been analyzed with a parameter-fitting model that assumes four sources of luminosity: a white dwarf primary star, a main-sequence secondary star, a flared accretion disk with a rim, and a bright spot at the intersection of the mass transfer stream and the disk periphery. A matrix of model solutions have been computed, covering an extensive range of plausible parameter values. The solution matrix was then explored to determine the optimum values for the fitting parameters and their associated errors. For models that treat the accretion disk as a flat structure without a rim, optimum fits require that the disk have a flat temperature profile. Although models with a truncated inner disk (R_in >> R_wd) resulted in a steeper temperature profile, steady-state models with a temperature profile characterized by T(r) \propto r^{-3/4} are found only for models with a significant disk rim. It is suggested that the flat temperature profiles found in some previous studies of disks in novae, erupting dwarf novae, and novalike systems may have resulted from failure to consider the effect of a disk rim. A comparison of the observed brightness and color at mid-eclipse with the photometric properties of the best-fitting model suggests that V Per lies at a distance of ~ 1 kpc.