  In this work we study the interactions of bottom mesons which lead to
$\Upsilon$ production and absorption in hot hadronic matter. We use effective
Lagrangians to calculate the $\Upsilon$ production cross section in processes
such as $ \bar{B}^{(*)} + B^{(*)} \to \Upsilon + (\pi, \rho)$ and also the
$\Upsilon$ absorption cross section in the corresponding inverse processes. We
update and extend previous calculations by Lin and Ko, introducing anomalous
interactions. The obtained cross sections are used as input to solve the rate
equation which allows us to follow the time evolution of the $\Upsilon$
multiplicity. In contrast to previous conjectures, our results suggest that the
interactions in the hadron gas phase strongly reduce the $\Upsilon$ abundance.
