  We study a class of nonequilibrium lattice models which describe local
redistributions of a globally conserved energy. A particular subclass can be
solved analytically, allowing to define a temperature T_{th} along the same
lines as in the equilibrium microcanonical ensemble. The
fluctuation-dissipation relation is explicitely found to be linear, but its
slope differs from the inverse temperature T_{th}^{-1}. A numerical
renormalization group procedure suggests that, at a coarse-grained level, all
models behave similarly, leading to a two-parameter description of their
macroscopic properties.
