We investigate the feasible limits for realizing a continuously evaporated atom laser with high-temperature sources. A plausible scheme for realizing a truly continuous atom laser is to outcouple atoms from a partially condensed Bose gas while continuously reloading the system with noncondensed thermal atoms and performing evaporative cooling. Here we use quantum kinetic theory to model this system and estimate feasible limits for the operation of such a scheme. For sufficiently high temperatures, the figure of merit for the source is shown to be the phase-space flux. The dominant process limiting the usage of sources with low phase-space flux is the three-body loss of the condensed gas. We conclude that certain double-magneto-optical trap sources may produce substantial mean condensate numbers through continuous evaporation and provide an atom laser source with a narrow linewidth and reasonable flux.