The USDOE has spent millions of dollars over many years to develop HTE. They have had some success in defining the answers you seek. Most of this work is connected with support for the oil industries adaptation to hydrogen as an automotive fuel to replace oil in the future. Use the Internet to follow their work.

Start your own research by getting a book from J. J. Thomson Dated 1903 tatled, "Conduction of Electricity Through Gases (1903). In this book which was written by Thomson himself, you will find many clues relative to the effects of heat and electrolysis, and several testbed designs for experiments with electrons.

Good luck in a very interesting journey.