A novel approach to producing composite parts using thermoplastic-matrix tapes is described. A thermal analysis is presented for the case of focused heat sources such as lasers for melting and consolidating the prepregs in a continuous manufacturing process. A numerical grid generation method is employed to account for the complex geometry of the solution domain. Heat transfer is modeled using an orthotropic domain made of two-dimensional, continuous fiber anisotropic laminates. Heat of crystallization melting/solidification are included in the form of a heat generation term. The temperature distributions and thermal histories in the laminated composites are presented for varying consolidation speeds. The effects of preheating the consolidated laminate are investigated and the overall feasibility of the proposed process is discussed.