A two-dimensional double Multiple-Relaxation-Time thermal lattice Boltzmann method is used to simulate natural convection flows in differentially heated cavities. The buoyancy effects are considered under the Boussinesq assumption. Flow and temperature fields are respectively solved with nine and five discrete velocities models. Boundary conditions are implemented with the classical bounce-back or a ''on-node'' approach. The latter uses popular Zou and He and Counter-Slip formulations. This paper evaluates the differences between the two implementations for steady and time-dependent flows as well as the space and time convergence orders.