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 $zgtrsim 7.8$ 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.
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