  This paper consider the mesoscopic limit of a stochastic energy exchange
model that is numerically derived from deterministic dynamics. The law of large
numbers and the central limit theorems are proved. We show that the limit of
the stochastic energy exchange model is a discrete heat equation that satisfies
Fourier's law. In addition, when the system size (number of particles) is
large, the stochastic energy exchange is approximated by a stochastic
differential equation, called the mesoscopic limit equation.
