Turbulent natural convection in a large-scale cavity has taken a great attention thanks to its importance in many engineering applications such as building. In this work, the lattice Boltzmann method (LBM) is used to simulate turbulent natural convection heat transfer in a small room of housing heated from below by means of a heated floor. The ceiling and the four vertical walls of the room are adiabatic except for a portion of one vertical wall. This portion simulates a glass door with a cold temperature θ_{c} = 0. The cavity is filled by air (Pr = 0.71) and heated from below with uniformly imposed temperature θ_{h} = 1. The effects of the heat source length (Lr) and Rayleigh number (Ra) on the flow structure and heat transfer are studied for ranges of 0.2 ≤ Lr ≤ 0.8 and 5 × 10^{6} ≤Ra ≤ 10^{8}. The heat transfer is examined in terms of local and mean Nusselt numbers. The results show that an increase in Rayleigh number or in heat source length increases the temperature in the core of the cavity. The flow structure shows that turbulent natural convection regime is fully developed for Ra = 10^{8}. Correlations for mean Nusselt number as a function with Ra for different values of Lr are expressly derived.