"Thyme" is odd because it used to be spelled "tyme" in Middle English (1066-1400s). I assume it was changed to 'th' to be more similar to Latin and French. Something similar happened to "island" (iland) and "isle" (ile) where a silent 's' was added to make the words closer to the Latin "insula".
'th' is only an aspirated 't' for loan words in English. Most English words pronounce 'th' as the fricatives /θ/ or /ð/.
https://en.wikipedia.org/wiki/Th_(digraph)
"Thyme" is odd because it used to be spelled "tyme" in Middle English (1066-1400s). I assume it was changed to 'th' to be more similar to Latin and French. Something similar happened to "island" (iland) and "isle" (ile) where a silent 's' was added to make the words closer to the Latin "insula".
https://en.wiktionary.org/wiki/thyme
https://en.wiktionary.org/wiki/isle