In the current paper, a two-phase and two-dimensional model describing heat and water transfer in a packed-bed bioreactor (PBB) for solid-state fermentation (SSF) is proposed. The model considers most of the transport mechanisms taking place in solid and gas phases and for axial and radial directions. For simulation, realistic physical properties of the particles and of the bed were employed, as well as interface coefficients were calculated based on classical correlations. The case-study was the solid-state cultivation of the newly isolated thermophilic fungus Myceliophthora thermophila I-1D3b in a mixture of sugarcane bagasse (SCB) and wheat bran (WB) within a narrow cylindrical and jacketed PBB. For non-saturated aeration, results showed that substrate drying near the inlet of the bioreactor harms fungal growth. For narrow PBB, jacket plays important rule on heat removal; for large-diameter PBB, radial heat removal becomes negligible. Simulated results agreed with experimental ones. The novel model here proposed is a powerful tool for guiding the scale-up of PBB for SSF.