Consider a particle sitting at a fixed position outside of a stable black hole. If the system is heated up, the black hole horizon grows and there should exist a critical temperature above which the particle enters the black hole interior. We solve a simple model describing exactly this situation: a large $N$ matrix quantum mechanics modeling a fixed D-particle in a black hole background. We show that indeed a striking phenomenon occurs: above some critical temperature, there is a Bose-Einstein condensation of massless strings. The transition goes along with a drastic change in the long time behaviour of a two-point function.
