If you're speaking of the thermal printing process, no.
The thermal part of the process works a bit like a laser printer.
The "ink" is a roll of thin black plastic. It is thermally "welded" to the plastic tag or label.
If you look at the "ink" roll after it does a transfer you will see all of the plastic "ink" missing from the roll.
I believe you are thinking of the old thermal paper used in 80s TI calculator printers.
Edit to add a few details.