The ions and the electrons don't necessarily have the same temperature (non-thermal plasma), but if you leave them for a while, they will undergo equilibration. I would not overestimate the value in Kelvins of different degrees of freedom of subsystems. The temperature is associated with a mean kinetic energy. If you tackle an electron, you can accelerate it easily because of its low mass. Conversely, even a fast electron will not give raise to the same momentum transfer as a heavy particle. So a fast electron is "not as powerful" as an equally fast ion.
If you have an application like the ball, there the effect is mainly generated by accelerating of electrons in the electric field. If you go away from the electrodes, the field gets weaker and there the electrons lose their kinetic energy due to collisions with heavier particles. This is why a too high particle density (or pressure) is not the friend of open corona discharges - the glow effect can't extend too far away without an opposing charge somewhere else, such that there is a relevant electric field in between. Of course, if the temperature is generally high (thermal plasma) as in the sun, then you will have charges flying around in any case. But for the earthly applications you have in mind, the area containing free electrons/ions doesn't extend forever and the temperature will not kill you unless the electric field that produced it is super strong.
Then as Shaktyai pointed out, plasmas are not always totally ionized, usually the opposite is the case. For some cases the Saha equation holds and there you get an idea about the functional dependence of the ionization degree with temperature. For high $T$, the factor goes against 1 (graph exp(-1/x) in wolfram alpha or so).