The GT 240 will be fine with the current 350w PSU.
Delta Electronics is one of the better OEM power supply manufacturers.
True I´ve been done some research and I´ve found the Amps in the 12 V rail
+3.3V 15A, +5V 13A, +12V1 18A, +12V2 18A, -12V 0.8A, +5VSB 2.0A .
This PSU would handle easily a GT 240.