The parametric excitation of large-scale convective cells in non-uniform dusty plasmas with non-zero ion temperature is considered. A set of two coupled nonlinear equations (for the variation of the electrostatic potential and the ion pressure) governing the nonlinear dynamics of ion-drift waves in dusty plasmas (IDWDPs) is obtained. The equations are then simplified by using a standard multiscale expansion technique. A nonlinear dispersion relation, which describes the nonlinear electrostatic and thermal convective cells, is obtained. The analysis of our dispersion relation shows that only the electrostatic mode yields a non-zero growth rate. The thermal convective cell is found to be stable. A simple expression for the maximum instability growth rate and the optimal dimension of the convective mode is deduced. The fastest growing wave appears to be a zero-frequency mode, elongated perpendicularly to the plasma inhomogeneity. The electrostatic convective cell growth rate is compared with that for the traditional parametric IDWDP decay.