Despite the fact that axions are still elusive and hypothetical particles, they provide the most elegant solution to the strong CP problem and are also very compelling candidates for the missing (dark) matter. Axions can be copiously produced in the early universe via thermal processes, contributing to the mass-energy density of thermal hot relics, alike massive neutrinos. We analyze the mixed hot dark matter scenario considering both massive neutrinos and thermal axion species in light of the most recent cosmological observations. The tightest 95% CL limit on the axion mass is ma < 0.192 eV, four times smaller than in previous analyses. Interestingly, the most constraining 95% CL upper bound on the total neutrino mass within this mixed hot dark matter scenario is mν < 0.08 eV, well below the inverted neutrino mass ordering prediction. Would future axion searches find evidence for scenarios with thermal axions such that ma 0.3 eV, this would favor the normal ordering as the one governing the mass pattern of neutral fermions. If, on the other hand, future terrestrial double beta decay and/or long baseline neutrino experiments find that the nature mass ordering is the inverted one, this could rule out a wide region in the currently allowed thermal axion window. Our results therefore strongly support multi-messenger searches of axions and neutrino properties, together with joint analyses of their expected sensitivities.