~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 awoke troubled by a dream and an astrological omen that a leader of a circumcising people would arise and challenge him. His senators suggested it concerned only the Jews, but before he could act, Dihyah al-Kalbi arrived at his court with a message from the Prophet ﷺ and was found to be circumcised. Heraclius then wrote to a fellow scholar (most likely John IV). He later summoned his senators and asked what they thought of him embracing Muhammad ﷺ's faith; they reacted with fury, so he told them he was only testing their loyalty and remained upon his faith, dying 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.