In muon spin rotation experiments, the diamagnetic fraction observed at low temperatures is a consequence of the muon interaction with the lattice during the incorporation process and depends on the properties of the material. An increase of the diamagnetic fraction with decreasing temperature is observed in some cases, which we attribute to a thermal spike at the end of the muon trajectory. The thermal spike is due to energy liberated not only during the muon stopping process but also as a consequence of the stress release when the electron bound to a muon in a unrelaxed configuration jumps to a neighboring lattice site. The magnitude and time extension of this effect is more significant for highly disturbed lattices which exhibit very low thermal conductivities at low temperatures. A phenomenological description of some selected examples is presented, together with a discussion about heat transport, using existing models for the thermal spike.