  We discuss the efficiency of Monte Carlo methods in solving continuum
radiative transfer problems. The sampling of the radiation field and
convergence of dust temperature calculations in the case of optically thick
clouds are both studied. For spherically symmetric clouds we find that the
computational cost of Monte Carlo simulations can be reduced, in some cases by
orders of magnitude, with simple importance weighting schemes. This is
particularly true for models consisting of cells of different sizes for which
the run times would otherwise be determined by the size of the smallest cell.
We present a new idea of extending importance weighting to scattered photons.
This is found to be useful in calculations of scattered flux and could be
important for three-dimensional models when observed intensity is needed only
for one general direction of observations. Convergence of dust temperature
calculations is studied for models with optical depths 10-10000. We examine
acceleration methods where radiative interactions inside a cell or between
neighbouring cells are treated explicitly. In optically thick clouds with
strong self-coupling between dust temperatures the run times can be reduced by
more than one order of magnitude. The use of a reference field was also
examined. This eliminates the need for repeating simulation of constant sources
(e.g., background radiation) after the first iteration and significantly
reduces sampling errors. The applicability of the methods for three-dimensional
models is discussed.
