  A continuous wave atom laser formed by the outcoupling of atoms from a
trapped Bose-Einstein condensate (BEC) potentially has a range of metrological
applications. However, in order for the device to be truly continuous, a
mechanism to replenish the atoms in the BEC is required. Here we calculate the
temporal coherence properties of a continuously pumped atom laser beam
outcoupled from a trapped Bose-Einstein condensate which is replenished from a
reservoir at finite temperature. We find that the thermal fluctuations of the
condensate can significantly decrease the temporal coherence of the output beam
due to atomic interactions between the trapped BEC and the beam, and this can
impact the metrological usefulness of the device. We demonstrate that a Raman
outcoupling scheme imparting a sufficient momentum kick to the atom laser beam
can lead to a significantly reduced linewidth.
