A solution for the temperature profile in a cylindrical capillary evaporator subject to a uniform heat flux prior to the initiation of boiling is derived using the Green's Function method. An approximate solution is also derived for the case in which the evaporator is heated by means of a constant conductance to a heat dissipating device. The results of the analysis allow for the determination of applied power levels for which nucleation is likely to occur only within the vapor grooves of the evaporator while maintaining subcooling in the liquid core, thereby increasing the likelihood of a successful startup. Also, limits are found for which additional increases in the applied heat flux do not increase the temperature difference between the vapor grooves and the wick-liquid core interface. Several advantages of larger diameter evaporators observed experimentally in startup are explained and quantified by the model. This analysis is appropriate for standard capillary pumped loop evaporators during a fully-flooded startup as well as starter pump designs and loop heat pipes.