Two-dimensional numerical simulations of mantle convection with temperature and pressure dependent viscosity are used to study plume--lithosphere interaction beneath a fast moving plate. Plumes behavior and, hence, their erosional and melting potential, depend on the Rayleigh number and plume buoyancy flux. Analysis of the balance between large-scale and plume-induced flow and of the ability of the plume to melt allows to put bounds on the upper mantle viscosity (1020, 1021 Pas), on the plumes diameter (<200 km) and temperature anomaly (200--400¿C). Within this range of parameters, strongly time-dependent small-scale instabilities form in the plume-lithosphere boundary layer. They lead to thermal rejuvenation of the lithosphere downstream from the plume. The 1200¿C isotherm is raised by up to 30km, but the 800¿C isotherm is hardly moved, leading to a steep transient geotherm at the base of the plate.