'Th' in German is pronounced 't', thus thaler= täler, Thiergarten= Tier..., etc.

Thyme originated with Greek thymon, the 'h' is silent in modern Greek as well.
Thyme, Oxford English Dictionary, is pronounced tyme, which is one of the alternate spellings. (They show this with that phonetic reverse e, which I don't know how to do)
Thyme, Webster's Collegiate Dictionary, is pronounced 'tim, but "also thim." (long i, thus time or thime).

Guest markhf is also correct about that feature of Hiberno-English.

'Th' is absent in Spanish, but thyme becomes tomillo, thus they don't have to worry about it.