  Energy transport equations are derived directly from full molecular dynamics
models as coarse-grained description. With the local energy chosen as the
coarse-grained variables, we apply the Mori-Zwanzig formalism to derive a
reduced model, in the form of a generalized Langevin equation. A Markovian
embedding technique is then introduced to eliminate the history dependence. In
sharp contrast to conventional energy transport models, this derivation yields
{\it stochastic} dynamics models for the spatially averaged energy. We discuss
the approximation of the random force using both additive and multiplicative
noises, to ensure the correct statistics of the solution.
