Abstract: One of the targets of future cosmic microwave background (CMB) and baryon acoustic oscillation measurements is to improve the current accuracy in the neutrino sector and reach a much better sensitivity on extra dark radiation in the early Universe. In this paper, we study how these improvements can be translated into constraining power for well-motivated extensions of the standard model of elementary particles that involve axions thermalized before the quantum chromodynamics (QCD) phase transition by scatterings with gluons. Assuming a fiducial Lambda cold dark matter cosmological model, we simulate future data for Stage-IV CMB-like and Dark Energy Spectroscopic Instrument (DESI)-like surveys and analyse a mixed scenario of axion and neutrino hot dark matter. We further account also for the effects of these QCD axions on the light element abundances predicted by big bang nucleosynthesis. The most constraining forecasted limits on the hot relic masses are m(a) less than or similar to 0.92 eV and n-ary sumation m(nu) less than or similar to 0.12 eV at 95 per cent Confidence Level, showing that future cosmic observations can substantially improve the current bounds, supporting multimessenger analyses of axion, neutrino, and primordial light element properties.