Finnish has only 3 words, all loanwords that didn't drop the h: thai (+ thai food, thai boxing etc), theeta (name of the Greek letter) and thorax (medical term, common word is rintakehä).

https://www.kielitoimistonsanakirja.fi/#/th?searchMode=all

That's surprising to me, perhaps because "th" appears in inflected words such as "ovathan", dialectal words such as "vasthaan", compound words such as "oluthana" and names such as "Elisabeth" or "Porthania".

Also, I wonder what's the share of the pronounciations "t", "th" and "θ" in the word "theremin".

(You can download a list of word forms encountered in some selected written texts here: https://kaino.kotus.fi/sanat/taajuuslista/parole.php)

I only searched for 'th' in the beginning of the word. We can add these to the previous result:

triathlon, smoothie, maybe also apartheid

Also the dictionary finds huithapeli, häthätää, rustholli, but I don't think these have 'th' as a phoneme.

https://www.kielitoimistonsanakirja.fi/#/*th*?searchMode=onl...

Nice new findings in the dictionary!

What do you mean by having 'th' as a phoneme? If you mean the sound "θ", I don't think any of the words are pronounced with one in Finnish, typically. Rather, they have a "t" sound followed by a "h", or just a "t".