Numerical models show that small-scale convection (SSC) occurring atop a mantle plume is a plausible mechanism to rejuvenate the lithosphere. The triggering of SSC depends on the density contrast and on the rheology of the unstable layer underlying the stagnant upper part of the thermal boundary layer (TBL). Partial melting may change both properties. We analyze, using 2-D numerical simulations, how partial melting influences the dynamics of time-dependent SSC instabilities and the resulting thermo-mechanical rejuvenation of an oceanic plate moving atop of a plume. Our simulations show a complex behavior, with acceleration, no change, or delay of the SSC onset, due to competing effects of the latent heat of partial melting, which cools the plume material, and of the buoyancy increase associated with both melt retention and depletion of residue following melt extraction. The melt-induced viscosity reduction is too localized to affect significantly SSC dynamics. Faster SSC triggering is promoted for low melting degrees (low plume temperature anomalies, thick lithosphere, or fast moving plates), which limit both the temperature reduction due to latent heat of melting and the accumulation of depleted buoyant residue in the upper part of the unstable layer. In contrast, high partial melting degrees lead to a strong temperate decrease due to latent heat of melting and development of a thick depleted layer within the sublithospheric convecting layer, which delay the development of gravitational instabilities. Despite differences in SSC dynamics, the thinning of the lithosphere is not significantly enhanced relatively to simulations that neglect partial melting.