The vortex phase diagram in the external rotation frequency versus temperat
ure is calculated for dilute Bose-Einstein condensed gases. It is determine
d within the Bogoliubov-Popov theory for a finite temperature where the con
densate and noncondensate fractions are treated on an equal footing. The te
mperature dependences of various thermodynamic instability lines for the vo
rtex nucleation are computed to construct the phase diagram. Experiments ar
e proposed to resolve a recent controversy on the vortex creation problem a
ssociated with the quantized vortex observation in Rb-87 atom gases.