The core of zoroastrian morality is
"Good thoughts, good words, good actions"
and there is a christian prayer said during masses that goes:
"I confess to you my brothers and sisters that I have sinned, with my thoughts, with my words, with my actions, and with what I omitted to do, that's why I beg to you my brothers and sisters, and to God almighty, to intercede for me. Amen".
I found several versions of that prayer, but those three things: thoughts, words, and actions, are always there, always in that order. Could it be that this is Zoroastrian influence?.
I imagine that using familiar wording of key concepts would help t attract new converts, several early saints were either manicheist or zoroastrian converts, so maybe they used phrases common in their former religions and that flowed into the rest of christianity.
Even the part were christians say "with my actions and with what I omitted to do" seems like a reflection or a commentary on the zoroastrian doctrine, the idea that not doing the right thing is as bad as doing a bad thing, which maybe many zoroastrians rejected.
But maybe I'm reading to much into a small coincidence.
Good quesiton. We can look at some excerpts of the prayers in the Khordeh Avesta.
Padyab-Kusti:
Ohrmazd, Lord! I am contrite for all sins and I desist from them, from all bad thoughts, bad words and bad acts which I have thought, spoken or done in the world, or which have happened through me, or have originated with me. For those sins of thinking, speaking and acting, of body and soul, worldly or spiritual, O Ohrmazd! I am contrite, I renounce them. With three words I distance myself (from them).
...
I profess myself a Mazda-worshipper, a Zoroastrian, having vowed it and professed it. I pledge myself to the well-thought thought, I pledge myself to the well-spoken word, I pledge myself to the well-done action.
Ohrmazd Yasht:
I praise well-thought, well-spoken, and well-done thoughts, words, and deeds. I embrace all good thoughts, good words, and good deeds; I reject all evil thoughts, evil words, and evil deeds.
There is certainly some resemblance here. The question is how far back the phrase traces in Christian usage. The first I have been able to track down is from Clemetn of Alexandria, who seems to have been a fan of this concept:
Let everything you do be done for God, both deeds and words; and refer all that is yours to Christ; and constantly turn your soul to God; and lean your thought on the power of Christ
Cultivate quietness in word, quietness in deed, likewise in speech and gait; and avoid impetuous eagerness, for then the mind will remain steady, and will not be agitated by your eagerness
“What reason is there in the law's prohibiting a man from "wearing woman's clothing?" Is it not that it would have us to be manly, and to be effeminate neither in person and actions, nor in thought and word ? For it would have the man, that devotes himself to the truth, to be masculine both in acts of endurance and patience, in life, conduct, word, and discipline by night and by day; even if the necessity were to occur, of witnessing by the shedding of his blood.”
I am not terribly well-versed on the early Church Fathers, but Clement apparently took a great interest in Jewish esotericism and "mystery religions". Both of those traditions were influenced to vairous degrees by Zoroastrianism, so that is one plausible vector he may have picked it up by.
That said, a somewhat similar sentiment shows up in Colossians, dating to the 1st century AD:
And whatever you do, whether in word or deed, do it all in the name of the Lord Jesus, giving thanks to God the Father through him.
But it does not include "thought" - "in word and deed" is a phrase that Plato, various stoics and other classical writers used. It is notable that it seems to be common to this day to read the word/thought/deed sentiment into various passages in the Bible, even though it doesn't actually appear explicitly. This does tentatively suggest that it is an external concept that made its way into early theology.
Absent other evidence, I would suggest it possible that either Clement or someone else picked up the concept from either Jewish or Pagan esoteric movements influenced by Zoroastrianism. Alternatively, it could have been a development from the Greek "word and deed" phrase.