This list, compiled by R' Shimon Buchnik (a Sephardi rav in Chashmonaim) says one should recite "עצי בשמים" on thyme (בת קורנית), as you suggest.
However, this source (from R' David Lau) says that the custom is to recite "עשבי בשמים" on thyme1 even though he says that one would think you should recite "מיני בשמים".
Reiach HaSadeh (by R' Hanoch Slatin, p. 142) indicates that one should recite "מיני בשמים". The reason given is that, since thyme is primarily used as a seasoning in foods, there is a possibility that one should recite "הנותן ריח טוב בפירות", which is the appropriate blessing for enjoying the fragrance of edible fruit.2 Due to uncertainty on this point, R' Slatin indicates that the generic form is preferred (based on a similar ruling from Mishna B'rura 216:16 and Sha'ar HaTziyun 216:12 regarding cloves and cinnamon).
1 I'm not certain why the custom would be to recite "borei isvei". Perhaps there is some botanical difference between the common thyme (Thymus vulgaris) and Thymus capitatus or Thymus bovei that commonly grow in Israel, and perhaps the "טימין" referred to by R' Lau is derived from one of the latter varieties.
2 There is some difference of opinion regarding the nusach of this blessing, and the Mishna B'rura (216:9) prefers "אשר נתן ריח טוב בפירות " (similar to the formulation of "שנתן" found in the Shulchan Aruch), referring to the creation of the fragrant quality of fruits in the past tense.