  We study a class of non-equilibrium lattice models describing local
redistributions of a globally conserved quantity, which is interpreted as an
energy. A particular subclass can be solved exactly, allowing to define a
statistical temperature T_{th} along the same lines as in the equilibrium
microcanonical ensemble. We compute the response function and find that when
the fluctuation-dissipation relation is linear, the slope T_{FD}^{-1} of this
relation differs from the inverse temperature T_{th}^{-1}. We argue that T_{th}
is physically more relevant than T_{FD}, since in the steady-state regime, it
takes equal values in two subsystems of a large isolated system. Finally, a
numerical renormalization group procedure suggests that all models within the
class behave similarly at a coarse-grained level, leading to a new parameter
which describes the deviation from equilibrium. Quantitative predictions
concerning this parameter are obtained within a mean-field framework.
