I believe this question could be asked in either the English Language, Legal, or History stack, but I believe the historical aspect of this question is, by far, the most interesting, and I think will find the widest interest on the History stack. I will be answering my question, but still hoping for other answers to add to what I have found. But first, background information.
I was researching an incident that happened in 1845 in Ballinhassig, Ireland. Modern accounts of this incident are in stark contrast to the newspaper accounts of the day found in the Cork Examiner and Southern Reporter and Cork Commercial Courier, which depict the incident as overzealous cops slaughtering innocent villagers. Modern accounts portray the people as the aggressors. Either way, what was argued in court was (as told via the two newspapers) that if a cop accidentally shoots an innocent bystander while intending to shoot a lawful target (i.e. an assailant) then the officer is not culpable for the innocent's death, and it calls this situation "chaud melee". This mention is found in the 14 July 1845 edition of the Cork Examiner (paywall). It says:
I googled "chaud melee" and wiktionary brought up "chaud-medley" with the alternative form "chaud-mellé". The definition given is "hot affray". Going back to Google, I found this article, titled "Chaud-mellé: A Sudden, Unplanned, Intense, Heated Fray". This article makes the argument that chaud melee was an ancient Scottish legal concept that granted someone remission for the crime of murder, so long as it could be proved that the murder was unpremeditated.
The source it gives is the 1826 "Dictionary of the Law of Scotland". The reference supports the claim. It says:
"CHAUD MELLE, is a term in our ancient law, applied to homicide committed on a sudden, and in heat of blood. The person guilty of this offence had the benefit of sanctuary, from which, however, he might have been taken for trial, but if he proved chaud melle, he was returned safe in life and limb."
The law dictionary goes on to say that the "privilege of sanctuary" was "abolished at the Reformation." And, then I believe it is saying that the concept was held onto, basically, to differentiate between degrees of murders.
Now, this article takes the law dictionary to mean that,
"Any chance encounter that suddenly went south seems fair game...As much as we have pub brawls that erupt today, Scotland in the 1400s and 1500s surely had its share. And it seems such encounters may have been covered by this law, protecting those who killed others in unfortunate situations."
This mass murder free-for-all, where all unpremeditated murders were given remission did not sit right with me. Even with all the violence in Scotland's history, it just sounds so contrary to a prosperous society. Of note, the law dictionary usage of the term sort of contradicts the usage in the 1845 paper. It could be argued that the first usage (in the 1845 Ballinhassig affair) is a special type of unpremeditated murder, but the way the lawyer puts it, it sounds like he is using to me a police officer accidentally shooting an innocent in a hot affray, because he is already being kind of shady in usurping a Scottish legal concept for an Irish trial. Admirably, the author of the Medium.com article admits, "I'm unable to find absolute specifics on this, by way of examples." Further adding, "I'd love to hear confirmation from that from any authorities on the matter." While, far from an authority, I hope to add clarity to the matter.
In order to do so, I searched the term on the British Newspaper Archive (paywall for most/it has some well-known editions available to the public).
The earliest mention I can find appears in the 7 May 1753 edition of The Scots Magazine (purportedly the oldest still operating magazine in existence, though it's operation has not been continuous). It being in Scotland matches the law dictionary. The article using the term is about the trial of James Stewart. The way it uses the term is thus:
"And, first, it will observed, that the murder is not said to have been committed from a sudden passion, or chaud mella, as the law expresses it, but to have been premeditated and resolved upon for some days before it was committed."
It does not say what the punishment should have been had it been a chaud mella. So, it would appear that this earliest mention agrees with the definition given in the Sottish law dictionary, not the first mention I found (in the 14 July 1845 Cork Examiner).
The next time the term pops up in the British Newspaper Archive is 25 years later, in the Caledonian Mercury, published in Midlothian, Scotland. This article is difficult for me to parse thanks to all the Latin (though, Google Translate does make it comprehensible), but, from what I gather, it does not use the term in the manner of the Irish 1845 use. It says, "...there was no forethought felony, but only casual chaud-melee."
The next use I find is in the 20 October 1827 London Evening Standard and is reprinted verbatim 10 days later in the Cork Constitution. Interestingly, the Cork Constitution is published in the same city that the Cork Examiner of 17 July 1845 was published in (in case you didn't know Cork was a city). Also, if you read the coverage of the "Ballinhassig Slaughter" in the Cork Examiner and Southern Reporter and Cork Commercial Courier, you will see that the lawyers involved in that case read the Cork Constitution. While I can't say for sure that is where the lawyers first encountered the term chaud melee, it is interesting to note that these lawyers, in 1845 at least, were reading the newspaper that first (as far as I can tell) printed this term in Ireland (the two prior usages were in Scotland and on in London) in 1827.
Now, the article is actually just a reproduction of the story "The Two Drovers", by Sir Walter Scott. I won't lie. By this time, everything was starting to seem monotonous and I was getting impatient, so I didn't read the whole article. Instead, I found a summary of the story on Wikipedia, which is just copied verbatim from [Henry Grey's 1882 book "A Key to All the Waverly Novels, in Chronological Sequence"] (https://www.google.com/books/edition/A_Key_to_All_the_Waverley_Novels_in_Chro/hJzgCzqBkcwC?hl=en&gbpv=1&dq=In+1795,+Robin+Oig+was+just+starting+from+Doune+with+a+drove+of+cattle+for+England&pg=RA1-PA28&printsec=frontcover). Taken together, the story tells of how two men got into an argument. One man hit the other, who fell to the ground unconscious. When he regained consciousness, he went and fetched his sword then stabbed his antagonist to death. At the trial, he plead chaudé melée; however, the judge determined that the 12-mile walk it took for him to retrieve his sword was enough for him to come to his senses, so chaudé melée was denied, and he was hanged for killing his aggressor.
I found a few other mentions, but all were used in the manner similar to the law dictionary, and provide no further insight. However, I changed up my search query and found something that provides more clarity on the subject. I will elaborate in an answer.