  We introduce well-defined characterizations of prethermal states in realistic
periodically driven many-body systems with unbounded chaotic diffusion of the
kinetic energy. These systems, interacting arrays of periodically kicked
rotors, are paradigmatic models of many-body chaos theory. We show that the
prethermal states in these systems are well described by a generalized Gibbs
ensemble based essentially on the average Hamiltonian. The latter is the
quasi-conserved quantity in the prethermal state and the ensemble is
characterized by the temperature of the state. An explicit exact expression for
this temperature is derived. Also, using arguments based on chaos theory, we
demonstrate that the lifetime of the prethermal state is exponentially long in
the inverse of the temperature. Our analytical results, in particular those for
the temperature and the lifetime of the prethermal state, agree well with
numerical observations.
