  We study magnetic, transport and thermodynamic properties of the half-filled
two-dimensional ($2D$) Hubbard model with layered distributed repulsive
interactions using unbiased finite temperature quantum Monte Carlo simulations.
Antiferromagnetic long-ranged correlations at $T=0$ are confirmed by means of
the magnetic structure factor and the onset of short-ranged ones is at a
minimum temperature which can be obtained by peaks in susceptibility and
specific heat following an RPA prediction. We also show that transport is
affected in the large interaction limit and is enhanced in the non-repulsive
layers suggesting a change of dimensionality induced by increased interactions.
Lastly, we show that by adiabatically switching the interactions in layered
distributed patterns reduces the overall temperature of the system with a
potential application in cooling protocols in cold atoms systems.
