Quantum interference effects play a vital role in shaping the linear polarization profiles of solar spectral lines. The Ba ii D 2 line at 4554Å is a prominent example, where the F -state interference effects due to the odd isotopes produce polarization profiles, which are very different from those of the even isotopes that have no F -state interference. It is therefore necessary to account for the contributions from the different isotopes to understand the observed linear polarization profiles of this line. Here we do radiative transfer modeling with partial frequency redistribution (PRD) of such observations while accounting for the interference effects and isotope composition. The Ba ii D 2 polarization profile is found to be strongly governed by the PRD mechanism. We show how a full PRD treatment succeeds in reproducing the observations, while complete frequency redistribution (CRD) alone fails to produce polarization profiles that have any resemblance with the observed ones. However, we also find that the line center polarization is sensitive to the temperature structure of the model atmosphere. To obtain a good fit to the line center peak of the observed Stokes Q/I profile, a small modification of the FALX model atmosphere is needed, by lowering the temperature in the line-forming layers. Because of the pronounced temperature sensitivity of the Ba ii D 2 line it may not be a suitable tool for Hanle magnetic-field diagnostics of the solar chromosphere, because there is currently no straightforward way to separate the temperature and magnetic-field effects from each other.