  We predict that triangle singularities of hadron spectroscopy can be strongly
affected in heavy ion collisions. To do it we examine various effects on the
singularity-inducing triangle loop of finite temperature in the terminal hadron
phase. It appears that peaks seen in central heavy ion collisions are more
likely to be hadrons than rescattering effects under two conditions. First, the
flight-time of the intermediate hadron state must be comparable to the lifetime
of the equilibrated fireball (else, the reaction mostly happens in vacuo after
freeze out). Second, the medium effect over the triangle-loop particle mass or
width must be sizeable. When these (easily checked) conditions are met, the
medium quickly reduces the singularity: at T about 150 MeV, even by two orders
of magnitude, acting then as a spectroscopic filter.
