ABSTRACT ALMA observations have revealed the presence of dust in galaxies in the Epoch of Reionization (EoR; redshift z > 6). However, the dust temperature, Td, 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 (GMCs), largely dominating the observed far-infrared luminosity, is warmer ($T_\mathrm{ d} \lower.5ex\hbox{$\,\, \buildrel\,\gt\, \over \sim \,\,$}60\ \mathrm{K}$) 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 $\sim 40$ per cent of the total UV radiation emitted by newly born stars remains obscured. A higher Td has additional implications: it (a) reduces the tension between local and high-z IRX–β relation, and (b) alleviates the problem of the uncomfortably large dust masses deduced from observations of some EoR galaxies.