  We construct an extension of the standard Kogut-Susskind lattice model for
classical 3+1 dimensional Yang-Mills theory, in which ``classical particle''
degrees of freedom are added. We argue that this will correctly reproduce the
``hard thermal loop'' effects of hard degrees of freedom, while giving a local
implementation which is numerically tractable. We prove that the extended
system is Hamiltonian and has the same thermodynamics as dimensionally reduced
hot Yang-Mills theory put on a lattice. We present a numerical update algorithm
and study the abelian theory to verify that the classical gauge theory
self-energy is correctly modified. Then we use the extended system to study the
diffusion constant for Chern-Simons number. We verify the Arnold-Son-Yaffe
picture that the diffusion constant is inversely proportional to hard thermal
loop strength. Our numbers correspond to a diffusion constant of Gamma = 29 +-
6 alpha_w^5 T^4 for m_D^2 = 11 g^2 T^2/6.
