  We consider the planar Ising model in a finite square box and we replace the
temperature parameter with a function depending on the magnetization. This
creates a feedback from the spin configuration onto the parameter, which drives
the system towards the critical point. Using the finite-size scaling results of
arXiv:0811.4507, we show that, when the size of the box grows to infinity, the
temperature concentrates around the critical temperature of the planar Ising
model on the square lattice.
