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We formulate a homogenized thermo-chemical model to simulate the manufacturing of unidirectional composites made of carbon fibers embedded in a thermosetting dicyclopentadiene (DCPD) matrix using frontal polymerization (FP). The reaction-diffusion model is then solved using the finite element method to investigate the evolution of the temperature and degree of cure during the fabrication process. The results reveal two different processing regimes: At lower fiber volume fractions, the polymerization front speed increases with the fiber volume fraction due to the increase in the effective thermal conductivity of the composite. At higher fiber volume fractions, the front velocity decreases with increasing fiber content due to the reduced heat source generated by the exothermic reaction. The 1-D simulations are complemented with 2-D studies that include heat losses to the surroundings. The model predictions are validated with experiments conducted on carbon/DCPD composite panels manufactured through frontal polymerization.