Recent tomographic imaging of the mantle below major hot spots shows slow seismic velocities extending down to the core-mantle boundary, confirming the existence of mantle plumes. However, these plumes are much thicker than previously thought. Using new laboratory experiments and scaling laws, we show that thermal plumes developing in a visco-plastic fluid present much larger diameters than plumes developing in a Newtonian fluid. Such a rheology requiring a yield stress is consistent with a lower mantle predominantly deforming by pure dislocation climb. Yield stress values between 1 and 10 MPa, implying dislocation densities between 10(8) and 10(10) m(-2), would be sufficient to reproduce the plumes morphology observed in tomographic images.