  A particular, two-dimensional, tiling model, composed by the so called Wang
tiles has been studied at finite temperature by Monte Carlo numerical
simulations. In absence of any thermal bath the Wang tiles give the opportunity
of building a very large number of non-periodic tilings. We can construct a
local Hamiltonian such that only perfectly matched tilings are ground states
with zero energy. This Hamiltonian has a very large degeneracy. The
thermodynamic behaviour of such a system seems to show a continuous phase
transition at non zero temperature. An order parameter with non-trivial
features is proposed. Under the critical temperature the model exhibits aging
properties. The fluctuation-dissipation theorem is violated.
