Sublithospheric small-scale convection (SSC) is thought to be responsible for the flattening of the seafloor depth and surface heat flow observed in mature plates. Although the existence of SSC is generally accepted, its ability to effectively produce a constant lithospheric thickness (i.e. flattening of observables) is a matter of debate. Here we study the development and evolution of SSC with a 2D thermomechanical finite-element code. Emphasis is put on (i) the influence of various rheological and thermophysical parameters on SSC, and (ii) its ability to reproduce geophysical observables (i.e. seafloor depth, surface heat flow, and seismic velocities). We find that shear heating plays no significant role either in the onset of SSC or in reducing the lithospheric thickness. In contrast, radiogenic heat sources and adiabatic heating exert a major control on both the vigour of SSC and the thermal structure of the lithosphere. We find that either dislocation creep, diffusion creep, or a combination of these mechanisms, can generate SSC with rheological parameters given by laboratory experiments. However, vigorous SSC and significant lithospheric erosion are only possible for relatively low activation energies.