We present the calculation of heavy Wilson quark mass renormalization const
ants from large beta Monte Carlo simulations. Simulations were performed at
various beta larger than 9, each on several spatial lattice sizes to allow
for an infinite volume extrapolation. We use twisted boundary conditions t
o suppress tunneling and work in Coulomb gauge with appropriate adjustments
for the temporal links. The one-loop coefficient obtained from this method
is in agreement with the analytical result and a preliminary result for th
e second order coefficient is reported.