~c. 7-8 AH
Details differ across the sources
Sh. Yasir Qadhi notes Bukhari records two distinct hadiths about Heraclius and the letter, this dream/senate scene and the separate Abu Sufyan interrogation, which did not happen the same day, though the exact chronology between them is uncertain.
Heraclius, the Roman emperor, once woke up troubled. He said that he had seen a dream, and that his astrologers had read an evil omen. A leader had appeared among a new people who practiced circumcision, and this leader would challenge him. His senators told him there was nothing to worry about. The only people who circumcised, they said, were the Jews, so he could simply impose harsher rules on them.
Before Heraclius could do this, Dihyah al-Kalbi arrived at his court with a letter from the Prophet ﷺ. Heraclius had him examined, and he was found to be circumcised. This made Heraclius deeply concerned, and he wrote to a friend about the matter, most likely John IV.
Later, Heraclius gathered his senators and asked what they would think if he accepted the faith of Muhammad ﷺ. They reacted with fury and said he would never remain their emperor. So Heraclius told them he had only been testing their faith, and that he would never leave Christianity. He died upon his faith some years later, in the middle of a coup.
Recorded in Sahih al-Bukhari as a separate hadith from the Abu Sufyan interrogation; per Sh. Yasir Qadhi this scene most likely took place a year or two apart from it, likely after the Tanukhi incident.
The Letters to the Kings·Chapter 6 of 6The senators of Rome
See the whole storyOther events recorded around the same time. Their order within the year is not established; use the storyline above for the sequence.
I have seen a dream, and my astrologers have foretold a very evil sign: a leader has appeared of a new people who will challenge me, and these people circumcise themselves.
Heraclius said this to a priest who had asked why he had woken in such a sad, anxious mood.
What do you think if I embrace Muhammad ﷺ's faith?
Heraclius posed this to his assembled senators after Dihyah al-Kalbi delivered the Prophet ﷺ's letter and Heraclius had grown privately convinced of his prophethood.
I was just testing your faith. I will never leave Christianity.