  If the thermal evolution of the hot young neutron star in the supernova
remnant HESS J1731-347 is driven by neutrino emission, it provides a stringent
constraint on the coupling of light (mass $\ll 10$ keV) axion-like particles to
neutrons. Using Markov-Chain Monte Carlo we find that for the values of
axion-neutron coupling $g_{ann}^2 > 7.7 \times 10^{-20}$ (90% c.l.) the axion
cooling from the bremsstrahlung reaction $n+n\rightarrow n+n +a$ is too rapid
to account for the high observed surface temperature. This implies that the
Pecci-Quinn scale or axion decay constant $f_a > 6.7 \times 10^7$ GeV for KSVZ
axions and $f_a > 1.7 \times 10^9$ GeV for DFSZ axions. The high temperature of
this neutron star also allows us to tighten constraints on the size of the
nucleon pairing gaps.
