Reddit mentions of Fisher-Price Thomas & Friends Wooden Railway, Train, Thomas - Battery Operated Train

You're looking for "battery operated" Thomas trains, not to be confused with the "Track Master" Thomas trains. They fit on the standard wooden track sets and move by themselves.
We have several and they work great. Kiddo loves them.
https://www.amazon.com/dp/B009NFFYWM/ref=cm_sw_r_cp_api_bUfoyb6MC52K6

This electric Thomas works with the wood tracks I described above.

Just realized I might have to pick this up for our boy now that I know it exists.

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