Yes, because the ionised gas molecules that bridge the gap between electrodes carry more energy. Frank and Harper have tested it up to around 200C. But it isn't thermal energy conversion 'as we know it' since the device is isothermal- no hot-cold junction.
Very interesting! I suggest to set up an experiment inside a well-controlled isothermal environment to obtain a table/function that shows the dependence of power output on the temperature
What happens at low temperatures?