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 high-energy sector, with a transverse field much bigger than the other, the 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 despite being initially above the critical temperature.