ALICE (A Large Ion Collider Experiment) is the LHC detector dedicated to the study of nucleus–nucleus collisions, in which the formation of the quark–gluon plasma (QGP) is expected. Heavy quarkonia, especially the Upsilon states, are relevant for studying the QGP since they provide an essential probe of the earliest and hottest stages of heavy ion collisions. They will be measured via their dimuon decay channel in ALICE in the muon spectrometer. The muon spectrometer performance has been studied in simulations, the results will be presented with emphasis on the trigger efficiency and rate in Pb–Pb collisions. The expected yields of Upsilon states will be extracted from a simulation based on a global fit of the dimuon mass spectra for different collision centralities.