  Standard decoupling of heavy fermions may fail when there are
non-perturbative variations in a scalar field which gives masses to the
fermions. One situation of phenomenological relevance is the case of sphalerons
in the presence of fermions at finite temperatures. The free energy of a simple
model is determined using a non-perturbative technique to study the effect of
fermions on the scalar field. The effects of quantum and thermal fermionic
fluctuations on the free energy of the thermal sphaleron are calculated,
including contributions from the gradients of the scalar field to all orders.
