We study nanoscale morphology of PbTe/CdTe multilayer heterostuctures grown by molecular beam epitaxy on hybrid GaAs/CdTe (100) substrates. Nominally, the structures consist of 25 repetitions of subsequently deposited CdTe and PbTe layers with comparable thicknesses of 21 and 8 nm, respectively. However, the morphology of the resulting structures crucially depends on the growth temperature. The two-dimensional layered, superlattice-like character of the structures remains preserved only when grown at low substrate temperatures, such as 230 °C. The samples grown at the slightly elevated temperature of 270 °C undergo a morphological transformation to structures consisting of CdTe and PbTe pillars and columns oriented perpendicular to the substrate. Although the pillar-like objects are of various shapes and dimensions these structures exhibit exceptionally strong photoluminescence in the near infrared spectral region. At the higher growth temperature of 310 °C, PbTe and CdTe separate completely forming thick layers oriented longitudinally to the substrate plane. The observed topological transformations are driven by thermally activated atomic diffusion in the solid state phase. The solid state phase remains fully coherent during the processes. The observed topological transitions leading to the material separation in PbTe/CdTe system could be regarded as an analog of spinodal decomposition of an immiscible solid state solution and thus they can be qualitatively described by the Cahn-Hillard model as proposed by Groiss et al (2014 APL Mater. 2 012105).