  We study preheating in models where a scalar inflaton is directly coupled to
a non-Abelian $SU(2)$ gauge field. In particular, we examine $m^2 \phi^2$
inflation with a conformal, dilaton-like coupling to the non-Abelian sector. We
describe a numerical scheme that combines lattice gauge theory with standard
finite difference methods applied to the scalar field. We show that a
significant tachyonic instability allows for efficient preheating, which is
parametrically suppressed by increasing the non-Abelian self-coupling.
Additionally, we comment on the technical implementation of the evolution
scheme and setting initial conditions.
