Based on a three-dimensional model of an early star-forming galaxy, we explore the evolution of the sub-millimetre brightness. The model galaxy is employed from an ultra-high-resolution chemodynamic simulation of a primordial galaxy by Mori & Umemura, where the star formation rate (SFR) is ∼10 M⊙ yr−1 at tage≲ 0.3 Gyr and several M⊙ yr−1 at tage >0.3 Gyr. The former phase well reproduces the observed properties of Lyman alpha emitters (LAEs) and the latter does Lyman break galaxies (LBGs). We solve the three-dimensional radiative transfer in the clumpy interstellar media in this model galaxy, taking the size distributions of dust grains into account, and calculate the dust temperature as a function of galactic evolutionary time. We find that the clumpiness of interstellar media plays an important role for the sub-millimetre brightness. In the LAE phase, dust grains are concentrated on clumpy star-forming regions that are distributed all over the galaxy, and the grains can effectively absorb ultraviolet (UV) radiation from stars. As a result, the dust is heated up to Tdust≳35 K. In the LBG phase, the continuous supernovae drive dust grains far away from star-forming regions. Then, the grains cannot absorb much radiation from stars, and become a cold state close to the cosmic microwave background (CMB) temperature. Consequently, the dust temperature decreases with the evolutionary time, where the mass-weighted mean temperature is Tdust= 26 K at tage= 0.1 Gyr and Tdust= 21 K at tage= 1.0 Gyr. By this analysis, it turns out that the sub-millimetre brightness is higher in the LAE phase than that in the LBG phase, although the dust-to-gas ratio increases monotonically as a function of time. We derive the spectral energy distributions by placing the model galaxy at a given redshift. The peak flux at 850 μ m is found to be S850∼ 0.2–0.9 mJy if the model galaxy is placed at 6 ≥z≥ 2. This means that Atacama Large Millimetre/sub-millimetre Array (ALMA) can detect an early star-forming galaxy with SFR of ∼10 M⊙ yr−1 by less than one hour integration with 16 antennas.