  We investigate the collective behavior of an Ising lattice gas, driven to
non-equilibrium steady states by being coupled to {\em two} thermal baths.
Monte Carlo methods are applied to a two-dimensional system in which one of the
baths is fixed at infinite temperature. Both generic long range correlations in
the disordered state and critical poperties near the second order transition
are measured. Anisotropic scaling, a key feature near criticality, is used to
extract $T_{c}$ and some critical exponents. On the theoretical front, a
continuum theory, in the spirit of Landau-Ginzburg, is presented. Being a
renormalizable theory, its predictions can be computed by standard methods of
$\epsilon $-expansions and found to be consistent with simulation data. In
particular, the critical behavior of this system belongs to a universality
class which is quite {\em different} from the uniformly driven Ising model.
