  The Murchison Widefield Array (MWA) team has derived new upper limits on the
spherically averaged power spectrum of the 21-cm signal at six redshifts in the
range $z \approx 6.5-8.7$. We use these upper limits and a Bayesian inference
framework to derive constraints on the ionization and thermal state of the
intergalactic medium (IGM) as well as on the strength of a possible additional
radio background. We do not find any constraints on the state of the IGM for
$z\gtrsim 7.8$ if no additional radio background is present. In the presence of
such a radio background, the 95 per cent credible intervals of the disfavoured
models at redshift $\gtrsim 6.5 $ correspond to an IGM with a volume averaged
fraction of ionized regions below 0.6 and an average gas temperature $\lesssim
10^3$ K. In these models, the heated regions are characterised by a temperature
larger than that of the radio background, and by a distribution with
characteristic size $\lesssim 10$ $h^{-1}$ Mpc and a full width at half maximum
(FWHM) of $\lesssim 30$ $h^{-1}$ Mpc. Within the same credible interval limits,
we exclude an additional radio background of at least $0.008\%$ of the CMB at
1.42 GHz.
