The use of relativistic electron beams for supplementary heating of tokamaks to ignition temperatures is discussed, under the assumption that they can be successfully injected. It is shown that if an electron beam with present-state-of-the-art power, but longer pulse length, can be injected into an Ohmically pre-heated tokamak plasma, it transfers its energy to the plasma on a time-scale short enough for synchrotron radiation to be an unimportant beam energy loss mechanism, while the turbulence generated does not affect the energy confinement. Beam energy and pulse characteristics required for an extension of the ideas to a reactor-size tokamak are presented.