  We present a quantum Monte Carlo investigation of the finite-temperature
phase diagram of the quantum dimer model on the square lattice. We use the
sweeping cluster algorithm, which allows to implement exactly the dimer
constraint, supplemented with a equal-time directed loop move that allows to
sample winding sectors. We find a high-temperature critical phase with
power-law correlations that extend down to the Rokshar-Kivelson point, in the
vicinity of which a re-entrance effect in the lines of constant exponent is
found. For small values of the kinetic energy strength, we find
finite-temperature transitions to ordered states (columnar and staggered) which
match those of interacting classical dimer models.
