  We investigate the dynamics brought on by an impulse perturbation in two
infinite-range quantum Ising models coupled to each other and to a dissipative
bath. We show that, if dissipation is faster the higher the excitation energy,
the pulse perturbation cools down the low-energy sector of the system, at the
expense of the high-energy one, eventually stabilising a transient
symmetry-broken state at temperatures higher than the equilibrium critical one.
Such non-thermal quasi-steady state may survive for quite a long time after the
pulse, if the latter is properly tailored.
