Questions & Answers about İçten teşekkür ederim.
In this sentence, it works adverbially.
Its basic meaning is something like sincere / heartfelt / from the heart, but here it modifies the act of thanking, so the sense is I thank you sincerely rather than the thanks are sincere.
This is common in Turkish: a word that looks adjective-like in English can often be used directly in an adverb-like way, without needing a separate -ly form.
Because Turkish has two different I letters:
- İ / i = a dotted letter
- I / ı = a dotless letter
These are separate letters in the alphabet, not just spelling variants.
So when içten is capitalized, it becomes İçten, not Içten.