Because of recently reported successes in the use of intense relativistic electron beams for heating toroidal plasmas, their application in Los Alamos Scientific Laboratory toroidal z-pinch experiments (ZT-40 and ZT-S) is examined. The conclusion is reached that a modestly sized beam (approx. k$150) could be useful for heating an experiment with the size of ZT-S, but that it would require a much larger beam to significantly effect the bulk temperature of larger experiments, such as ZT-40.