  We compute the topological susceptibility of $N_f=2+1$ QCD with physical
quark masses in the high-temperature phase, using numerical simulations of the
theory discretized on a space-time lattice. More precisely we estimate the
topological susceptibility for five temperatures in the range from $\sim200$
MeV up to $\sim600$ MeV, adopting the spectral projectors definition of the
topological charge based on the staggered Dirac operator. This strategy turns
out to be effective in reducing the large lattice artifacts which affect the
standard gluonic definition, making it possible to perform a reliable continuum
extrapolation. Our results for the susceptibility in the explored temperature
range are found to be partially in tension with previous determinations in the
literature.
