  In this paper we study macroscopic thermodynamic properties of a stochastic
microscopic heat conduction model that is reduced from deterministic problems.
Our goal is to numerically check how the `low energy site effect' inherited
from the deterministic model would affect the macroscopic thermodynamic
properties such as the thermal conductivity and the local thermodynamic
equilibrium. After a series of numerical computations, our conclusion is that
neither the thermal conductivity nor the existence of local thermodynamic
equilibrium is qualitatively changed by this effect.
