Answer
The temperature should increase.
Work Step by Step
The electron gas expands into vacuum, so the work done, and the heat added, is zero. The change of internal energy $\Delta U=0$.
As the electrons move farther apart, their potential energy decreases. The internal energy of the system is the same, so the electrons’ kinetic energy increases. This increases their temperature.
The situation is like letting a compressed spring expand, and the PE turning into KE.
