  We show in a simple exactly-solvable toy model that a properly designed
impulse perturbation can transiently cool down low-energy degrees of freedom at
the expenses of high-energy ones that heat up. The model consists of two
infinite-range quantum Ising models, one, the \textit{high-energy} sector, with
a transverse field much bigger than the other, the \textit{low-energy} sector.
The finite-duration perturbation is a spin-exchange that couples the two Ising
models with an oscillating coupling strength. We find a cooling of the
low-energy sector that is optimised by the oscillation frequency in resonance
with the spin-exchange excitation. After the perturbation is turned off, the
Ising model with low transverse field can even develop spontaneous
symmetry-breaking d
