  One alternative to the cold dark matter (CDM) paradigm is the scalar field
dark matter (SFDM) model, which assumes dark matter is a spin-0 ultra-light
scalar field (SF) with a typical mass $m\sim10^{-22}\mathrm{eV}/c^2$ and
positive self-interactions. Due to the ultra-light boson mass, the SFDM could
form Bose-Einstein condensates (BEC) in the very early Universe, which are
interpreted as the dark matter haloes. Although cosmologically the model
behaves as CDM, they differ at small scales: SFDM naturally predicts fewer
satellite haloes, cores in dwarf galaxies and the formation of massive galaxies
at high redshifts. The ground state (or BEC) solution at zero temperature
suffices to describe low-mass galaxies but fails for larger systems. A possible
solution is adding finite-temperature corrections to the SF potential which
allows combinations of excited states. In this work, we test the
finite-temperature multistate SFDM solution at galaxy cluster scales and
compare our results with the Navarro-Frenk-White (NFW) and BEC profiles. We
achieve this by fitting the mass distribution of 13 \textit{Chandra} X-ray
clusters of galaxies, excluding the region of the brightest cluster galaxy. We
show that the SFDM model accurately describes the clusters' DM mass
distributions offering an equivalent or better agreement than the NFW profile.
The complete disagreement of the BEC model with the data is also shown. We
conclude that the theoretically motivated multistate SFDM profile is an
interesting alternative to empirical profiles and ad hoc fitting-functions that
attempt to couple the asymptotic NFW decline with the inner core in SFDM.
