A mathematical model, based on the moving boundary approach, is developed for the growth of the deposit from paraffinic mixtures due to heat transfer in a pipeline. The model extends a recent study on the deposition from "waxy" mixtures by including unsteady-state energy balance and heat transfer in both radial and axial directions for hydrodynamically established laminar flow. Numerical solutions were obtained for the growth of deposit with time, both radially and axially, from a binary eutectic mixture of n-C16H34 and n-C28H58. Two different scenarios for the initiation of the deposition process were investigated. Even though the transient results for the temperature profile and deposit thickness differed significantly, identical steady-state predictions were obtained for the two scenarios. For a constant pipe-wall temperature, the steady-state deposit thickness was predicted to increase with the pipe length. The predicted deposit thickness was lower for a higher inlet mixture temperature, pipe-wall temperature, and Reynolds number. The trends in model predictions were compared with the published results from deposition experiments performed on similar waxy mixtures.