  We propose a scheme for constructing classical spin Hamiltonians from Hunds
coupled spin-fermion models in the limit J_H/t \to \infinity. The strong
coupling between fermions and the core spins requires self-consistent
calculation of the effective exchange in the model, either in the presence of
inhomogeneities or with changing temperature. In this paper we establish the
formalism and discuss results mainly on the ``clean'' double exchange model,
with self consistently renormalised couplings, and compare our results with
exact simulations. Our method allows access to system sizes much beyond the
reach of exact simulations, and we can study transport and optical properties
of the model without artificial broadening. The method discussed here forms the
foundation of our papers Phys. Rev. Lett. 91, 246602 (2003), and Phys. Rev.
Lett. 92, 126602 (2004).
