Abstract In this work we investigate the $$Z_b (10610)$$ Zb(10610) (called simply $$Z_b$$ Zb ) abundance in the hot hadron gas produced in heavy ion collisions after the quark–gluon plasma phase. We use effective Lagrangians to calculate the thermally averaged cross sections of $$Z_b $$ Zb production in processes such as $$B^{(*)} + \bar{B}^{(*)} \rightarrow \pi + Z_b (10610)$$ B(∗)+B¯(∗)→π+Zb(10610) and also of its absorption in the corresponding inverse processes. We then solve the rate equation to follow the time evolution of the $$Z_b$$ Zb multiplicity. We find that, if we neglect the $$Z_b$$ Zb decay, the number of $$Z_b$$ Zb ’s produced at the end of the quark–gluon plasma phase remains almost constant during the hadron phase. The introduction of the decay in the rate equation leads to a suppression in the final yield by a factor two.