  A constellation of quarkonium-mass peaks has been reported in the last
decade, opening what could be an entire new spectroscopy of nuclear-physics
like complexity. Salient among these structures are the $Z_c$, much analyzed at
BESIII as nicely summarised by J.~Zhao at this conference. Their stature as new
hadron states has often been challenged by proposals that the peaks arise from
triangle singularities instead, because they appear in three-body reactions and
often satisfy the special kinematic conditions of the Coleman-Norton theorem.
To experimentally decide, we should like to resort to different reactions
erasing the kinematic coincidence, and see whether each peak survives. We
observe that the most universal "eraser" is the medium created in Heavy Ion
Collisions, because its high temperature often affects the masses and widths of
the particles participating in the reaction: if additionally the triangle
reaction is completed during the lifetime of the fireball, our computations in
thermal field theory show that the triangle singularities do not survive the
hot hadron phase (much less the hotter quark-gluon plasma). On the contrary,
ordinary quarkonia are affected but often survive the fireball and
molecular-like states are also routinely detected. We have provided several
examples, and here investigate the exotic $Z_{c}(4020)^\pm\to \pi^{\pm} h_c $
peak (produced against a $\pi^\mp$ in $e^+e^-$ collisions). If, as has been
proposed during the debates, it is produced or enhanced by a $D_{1} D^{*} D^*$
triangle loop, the estimate here reported suggests its disappearance near the
critical temperature of the confinement/deconfinement phase transition, so any
future detection in heavy-ion collision data would suggest it to be a real
hadron, with its absence leaning towards the singularity interpretation.
