  Motivated by a heat radiative transport equation, we consider a particle
undergoing collisions in a space-time domain and propose a method to sample its
escape time, space and direction from the domain. The first step of the
procedure is an estimation of how many elementary collisions is safe to take
before chances of exiting the domain are too high; then these collisions are
aggregated into a single movement. The method does not use any model nor any
particular regime of parameters. We give theoretical results both under the
normal approximation and without it and test the method on some benchmarks from
the literature. The results confirm the theoretical predictions and show that
the proposal is an efficient method to sample the escape distribution of the
particle.
