The influence of controlled sawteeth on thermal helium exhaust is explored using the BALDUR 1½-dimensional transport code for an ARIES-I-type plasma. Sawteeth are shown to be useful for removing thermal helium from the central region to the outer region of a tokamak plasma. Outer region transport enhancement is found essential for removing the ash from the outer region. It is found that the optimal sawtooth period to give the minimum thermal helium level (or maximum fusion power) is several times larger than the fast alpha-particle slowing-down time for an ARIES-I-type driven plasma. With a sawtooth period of ~5 s and helium transport selectively enhanced by one order of magnitude relative to the diffusion of hydrogenic ions, the fusion power increases ~30% compared to the case without sawteeth/without enhancement. It is also found that sawteeth combined with outer region transport enhancement have the potential to advantageously reduce the helium concentration.