This paper discusses the extension of the perturbation boundary element method (BEM) described in the companion paper (Part 1) to transient-flow problems with permeability and porosity variations. The perturbation BEM formulated in Laplace space is verified against simplified heterogeneous problems and is used to generate type curves-for idealized heterogeneities. We observed that if the average property value in a drainage area was not much different from the near-well property value, heterogeneity had little effect on pressure responses.