A numerical formulation of the energy equation is developed for the laminar flow of a MEPCM fluid in a tube at a constant velocity and subjected to a constant and uniform wall heat flux. MEPCM fluids are phase-change fluids that are suspensions comprised of particles of microencapsulated phase-change material (MEPCM) in a carrier fluid. The thermodynamic behavior of MEPCM fluids is modeled for both melting and crystallization and included in an enthalpy formulation of the energy exchanges. A particular phase-change case involving a microPCM fluid is then solved for conditions that produce melting and crystallization of the phase-change material. Heat transfer results are presented which show that the MEPCM phase-change characteristics, along with system parameters, have significant effects on the potential of MEPCM fluids to improve heat transfer and facilitate enhanced temperature control in pumped loops.