The conventional hadron-resonance gas (HRG) model with the Particle Data Group (PDG) hadron input, full chemical equilibrium, and the hadron type dependent eigenvolume interactions is employed to fit the hadron mid-rapidity yield data of ALICE Collaboration for the most central Pb+Pb collisions. For the case of point-like hadrons the well-known fit result T = 154 ± 2 MeV is reproduced. However, the situation changes if hadrons have different eigenvolumes. In the case when all mesons are point-like while all baryons have an effective hard-core radius of 0.3 fm the χ 2 temperature dependence of the χ 2 has a broad minimum in the temperature range of 155 − 210 MeV, with fit quality comparable to the T ∼ 155 MeV minimum in the point-particle case. Very similar result is obtained when only baryon-baryon eigenvolume interactions are considered, with eigenvolume parameter taken from previous fit to ground state of nuclear matter. Finally, when we apply the eigenvolume corrections with mass-proportional eigenvolume vi ∼ mi, fixed to particular proton hard-core radius rp, we observe a second minimum in the temperature dependence of the χ 2 , located at the significantly higher temperatures. For instance, at rp = 0.5 fm the fit quality is better than in the point-particle HRG case in a very wide temperature range of 170 − 320 MeV, which gives an uncertainty in the temperature determination from the fit to the data of 150 MeV. These results show that thermal fits to the heavy-ion hadron yield data are very sensitive to the modeling of the short-range repulsion eigenvolume between hadrons, and that chemical freeze-out temperature can be extracted from the LHC hadron yield data only with sizable uncertainty.