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I have not found any information relating to using electicity to ionize air with temperature, but I am sure that there should be some information available. I am thinking of the nozzle of modern jet engine (about 2000℃)considering I don't have any sophisticated equipment.

Is there any way to measure or even calculate the energy(Joule) needed to maintain ionization of air at high temperature(2000℃)?

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    $\begingroup$ For clarity, how are you ionizing the air (thermal, electrical, chemical...) and how ionized (fraction) do you need it? $\endgroup$
    – Dan
    Mar 11, 2015 at 3:35
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    $\begingroup$ Well air is made up of a number of types of atoms/ molecules. The ionization potential for nitrogen is about 14.5 eV (according to this,environmentalchemistry.com/yogi/periodic/1stionization.html.) Temperature will only have a small effect, unless it get's very hot... kT is several eV. (kT is 25 meV, 0.025 eV at 300K.) $\endgroup$
    – George Herold
    Mar 11, 2015 at 18:28
  • $\begingroup$ Followup question: Are you interested in energy specifically (Joules) or are you looking for the voltage required to cause/sustain ionization. These are different problems with different answers. $\endgroup$
    – Dan
    Mar 11, 2015 at 20:59
  • $\begingroup$ @GeorgeHerold And what about the creation of the $N_2^+$ ions? Maybe it is easier as to produce nascens $N_2$ first, and then ionize it. $\endgroup$
    – peterh
    Mar 17, 2015 at 12:43

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As Herold has stated Nitrogen has a rather high ionization potential. However the voltage needed to ionize air depends on alot of other factors: density altitude humidity mean temperature presence of dust etc

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