Mineralization processes in ultramafic laterites are partly controlled by fluid flow regimes in these porous and permeable systems. During weathering of ultramafic rocks, exothermic chemical reactions, such as hydration of olivine, may generate shallow subsurface (< 200 m) temperatures of several tens of °C. The reaction-induced fracturing leads to further reactions and increases the permeability. For more than 20 Myr, the peridotite massifs of New Caledonia have undergone intense weathering, and the observable undulations along the weathering front, attest to a corrugated bedrock topography. Combined together, the excess heat (up to 70-90°C) and high permeability (10^-14 to 9 10^-13 m²) might have potentially triggered hydrothermal convection, as confirmed by Rayleigh number estimates. This was numerically modeled by accounting for temperature-dependent fluid properties, and for time-dependent and spatially varying parameters simulating the deepening of the weathering front. Modeling the transient evolution of the thermal and flow velocity fields over 10 Myr reveals that hydrothermal convection can develop in the New Caledonian laterites, even on sloped surfaces where topography-driven flow prevails. Convective cells develop above the weathering front, and the models reveal two-dimensional corrugations below which weathering is no longer efficient.