Simulation results of the thermal conductivity L of the Dissipative Particle Dynamics model with Energy Conservation (DPDE) are reported. We also present an analysis of the transport equations and the transport coefficients for DPDE based on a local equilibrium approximation. This approach is valid when the particle-particle thermal conductivity lambda and the friction coefficient zeta are large. A qualitative derivation of the scaling form of the kinetic contribution of the transport of energy is derived, yielding two different forms for the kinetic contribution to the heat transport, depending on the value of lambda. We find agreement between the theoretically predicted value for L and the simulation results, for large lambda and many particles interacting at one time. Significant differences are found for small number of interacting particles, even with large lambda. For smaller values of lambda, the obtained macroscopic thermal conductivity is dominated by diffusive transport, in agreement with the proposed scaling form.