Two closely related problems are discussed. I first apply to the Earth's mantle results of recent laboratory and theoretical modelling [ 1] of the fluid dynamics of the smallest scales of motion in thermal convection at high Rayleigh number. In the mantle, instabilities on a bottom boundary layer are likely to give rise to detached blobs called “thermals”. These are predicted to be approximately spherical masses of buoyant material which enlarge by entrainment of surrounding mantle as they rise. Thermals are most likely to have initial diameters of about 200 km and to rise through the full depth of an ideal uniform mantle in less than 10 8 years. On arrival at the base of the lithosphere their diameters may be up to 500 km, they still carry almost all of the heat with which they began and they induce temperature anomalies sufficient to cause partial melting. Predicted length and time scales indicate that this highly unsteady form of convection may be a plausible alternative to steady deep-mantle plumes as a cause of ocean island volcanism. Second, there is the possibility that localised regions of anomalous internal heating associated with chemical heterogeneities may lead to small scale convection as plumes or thermals. An analysis is presented for thermals in which all buoyancy is generated by internal heating. These thermals pass through a maximum temperature as a result of assimilation of cooler surrounding mantle. Using as an upper limit for anomalous internal heating that due to increased concentrations of radioactive elements in subducted oceanic basalts and sediments, it is shown that internal heating is of little consequence to the dynamics of chemical heterogeneities.