Abstract Green roofs are complex systems governed by intricate transport phenomena, which are frequently solved using simplified and empirical models. This paper describes a numerical model capable of solving the conservation equations that govern the unsteady nonlinear coupled moisture and heat energy transport through a multi-layer green roof composed of a structural support, a water storage layer, growing medium and canopy. To get an accurate insight into the role of different variables that affect the hygrothermal behaviour of green roofs, the temperature on the outer surface, as well as the outflow and inflow heat fluxes, were computed for different roof models and environmental conditions. A sensitivity analysis was performed to understand the role of the different layers and the canopy’s geometrical composition (e.g. vegetation coverage, plant height and leaf area index) in the energy balance of the building’s roof. Finally, to foresee the behaviour of the full canopy system under real climate conditions, weather data with distinct climatic characteristics from Braganca (Portugal) and Seville (Spain) were used. The simulated green roofs use insulation cork boards (ICBs) to replace both the water storage and insulation layers. Due to the intrinsic thermal characteristics of ICB (an ICB layer of 0.2 m allowed us to reduce the heat flux by about 58% compared with an ICB layer of 0.05 m), these roofs are expected to improve interior comfort and save energy. Although the ICB and soil layers made the greatest contribution to the thermal insulation, the characteristics of the vegetation were found to be of substantial importance to the overall performance of the green roof. The leaf area index (LAI) was the most relevant vegetation variable (a change from LAI = 2 to LAI = 5 decreased the inflow heat flux by about 27%), while difference in plant height did not lead to any significant change in inflow heat flux.