  In this paper we continue the study of perturbative renormalizations in an
$\mathcal{N}=(0,2)$ supersymmetric model. Previously we analyzed one-loop
graphs in the heterotically deformed CP$(N-1)$ models. Now we extend the
analysis of the $\beta$ function and appropriate $Z$ factors to two, and, in
some instances, all loops in the limiting case $g^2\to 0$. The field contents
of the model, as well as the heterotic coupling, remain the same, but the
target space becomes flat. In this toy $\mathcal{N}=(0,2)$ model we construct
supergraph formalism. We show, by explicit calculations up to two-loop order,
that the $\beta$ function is one-loop-exact. We derive a nonrenormalization
theorem valid to all orders. This nonrenormalization theorem is rather unusual
since it refers to (formally) $D$ terms. It is based on the fact that
supersymmetry combined with target space symmetries and "flavor"? symmetries is
sufficient to guarantee the absence of loop corrections. We analyze the
supercurrent supermultiplet (i.e., the hypercurrent) providing further evidence
in favor of the absence of higher loops in the $\beta$ function.
