  We compute the pressure, chiral condensate and strange quark number
susceptibility from first principles within perturbative QCD at finite
temperature and very high magnetic fields up to next-to-leading order and
physical quark masses. The region of validity for our framework is given by
$m_s \ll T \ll \sqrt{eB}$, where $m_s$ is the strange quark mass, $e$ is the
fundamental electric charge, $T$ is the temperature, and $B$ is the magnetic
field strength. We study the convergence of the perturbative series for the
pressure for different choices of renormalization scale in the running
coupling, $\alpha_s (T,B)$. Our results for the chiral condensate and strange
quark number susceptibility can be directly compared to recent lattice QCD data
away from the chiral transition. Even though current lattice results do not
overlap with the region of validity above, perturbative results seem to be in
the same ballpark.
