We present a computational model that predicts the consequences of time-dependent, isenthalpic assimilation-fractional crystallization (AFC). Our model combines an existing paradigm for fractional crystallization based on equilibrium thermodynamics with a kinetic model for predicting rates of mineral dissolution. The isenthalpic constraint directly links the sensible heat of the magma and the latent heat of crystallization to the energy necessary for assimilation. Thus, we predict liquid lines of descent, rates of crystallization, rates of cooling, and ratios of assimilation to crystallization (r) as a function of time. Model simulations predict the time scale of AFC processes (weeks to years) and show the extent to which temperature and composition of the assimilant control these time scales.