Heat propagation in quasi-one-dimensional materials (Q1DMs) often appears puzzling. For example, while an isolated Q1DM, such as a nanowire, a carbon nanotube, or a polymer, can exhibit a high thermal conductivity κ, forests of the same materials can show a reduction in κ. Until now, the complex structures of these assemblies have hindered the emergence of a clear molecular picture for this intriguing phenomenon. We combine coarse-grained simulations with concepts known from polymer physics and thermal transport to unveil a generic microscopic picture of κ reduction in molecular forests. We show that a delicate balance among the persistence length of the Q1DM, the segment orientations, and the flexural vibrations governs the reduction in κ.