  ALMA observations have revealed the presence of dust in galaxies in the Epoch
of Reionization (redshift $z>6$). However, the dust temperature, $T_d$, remains
unconstrained, and this introduces large uncertainties, particularly in the
dust mass determinations. Using an analytical and physically-motivated model,
we show that dust in high-$z$, star-forming giant molecular clouds (GMC),
largely dominating the observed far-infrared luminosity, is warmer ($T_d > 60\
\mathrm{K}$) than locally. This is due to the more compact GMC structure
induced by the higher gas pressure and turbulence characterizing early
galaxies. The compactness also delays GMC dispersal by stellar feedback, thus
$\sim 40\%$ of the total UV radiation emitted by newly born stars remains
obscured. A higher $T_d$ has additional implications: it (a) reduces the
tension between local and high-$z$ IRX-$\beta$ relation, (b) alleviates the
problem of the uncomfortably large dust masses deduced from observations of
some EoR galaxies.
