What's with the third degree?

Where did the phrase "third degree" (referring to intense interrogation) originate?

Additionally, how did "grill" come to have its related meaning?

Wikipedia has an article on third degree interrogation. Here are its hypotheses as to its origin:

No one knows the origin of the term but there are several hypotheses. [...]

Possible origins

• The third degree of Freemasonry and the rigorous procedures to advance to that level.
• The term may have been coined by Richard H. Sylvester, the Chief of Police for Washington, DC. He divided police procedures into the arrest as the first degree, transportation to jail as the second degree, and interrogation as the third degree.
• The term may have been coined by nineteenth century New York City Police detective Thomas F. Byrnes, perhaps as a pun on his name, as in third degree burns.

As an aside, you may be interested in this popular and related question.

Phrases.org seems more definite about the origin:

In Masonic lodges there are three degrees of membership; the first is called Entered Apprentice, the second Fellowcraft, and the third is master mason. When a candidate receives the third degree in a Masonic lodge, he is subjected to some activities that involve an interrogation and it is more physically challenging than the first two degrees. It is this interrogation that was the source of the name of the US police force's interrogation technique. That is referred to in an 1900 edition of Everybody's Magazine:

"From time to time a prisoner... claims to have had the Third Degree administered to him."

Answers.com and Dictionary.com seem to agree:

third degree
"intense interrogation by police," 1900, probably a reference to Third Degree of master mason in Freemasonry (1772), the conferring of which included an interrogation ceremony.

Grill meaning to subject to severe and persistent cross-examination is a metaphor. Imagine the examinee on a grill, being intensely "cooked" through by the questioning. Etymonline says its first usage in this sense is attested in 1894.

The earliest Elephind newspaper database matches that I've been able to find for "third degree" in the relevant sense suggest that a certain Inspector Byrnes of the New York Police Department developed the interrogation technique and gave it its name.

From "Arrest of a Gang of Burglars: Their Capture by Inspector Byrnes," in the New-York Tribune (February 5, 1883):

The Central Office detectives under the direction of Inspector Byrnes on Saturday arrested the gang of men who have been for two years sending out false fire alarms. They are all young., their ages ranging from seventeen to twenty-three years. When taken to Police Headquarters and put through what Inspector Byrnes styled "the third degree of initiation," or "pumping process," they all confessed their guilt.

From "Two Murderers Run Down: They Went to New Haven Monday Night and Killed Mrs. Ernst," in the [New York] Sun (May 13, 1887):

Chamberlin, who is a muscular young man nearly six feet tall, threw the detectives to one side and drew a revolver. The crowd scattered, but the detectives grappled with him, and while one knocked the pistol out of his hand the other knocked him down. In a twinkling he was on his feet again with a pair of steel bracelets on his wrists and was walking to Inspector Byrnes's office. Then Cora Bell was arrested in her room, and the Inspector had a long talk with the prisoners separately. Apparently he worked what his men call "the third degree racket" on them, for at 8 o'clock he looked and told the reporters that he was ready to tell them all about the murder. The Inspector's story was very complete, and he vouched for its correctness, but declined to say who had "squealed."

From "Did He Slay Lavarino? M'Carthy Now Claims That He Is an Innocent Man," in the [New York] Evening World (July 30, 1888):

John Luby, a burglar, who died in Auburn Prison in the fall of 1885, confessed on his death bed that he killed Lavarino, and McCarthy now writes to his wife Agnes, who resides in Eat One Hundred and Twelfth street, from his cell in Clinton Prison that Luby told the truth, that Luby was his friend and killed the man Lavarino in defense of McCarthy's life, and he (McCarthy) could do no less than return the favor by putting his life in peril to shield such a friend.

But McCarthy had made a confession, a "third degree' statement to Inspector Byrnes. The jury certainly thought it a confession, but in the light of subsequent events it can easily be seen how they may have been mistaken.

From "Masked Again in Court: Dress Rehearsal of the Attack on Big Phil Daly," in the [New York] Sun (December 8, 1888):

Inspector Byrnes took Hammond when he was sent back to Mulberry street and finished putting him through the third degree. ...

From "Dark for the Boy: Suspicion Points to Krulisch as the Drug Clerk's Murderer," in the [New York] Evening World March 9, 1889):

From there the prisoner was taken to the station-house and thence to Police Headquarters, where he was closeted with Inspector Byrnes who proceeded to give him his famous "third degree."

At 11 A.M. he took the boy in hand, and was still cross-questioning him at 12 o'clock noon.o'clock noon.

It is believed that the Inspector will get a full confession from him.

From "Two New York Arrests," in the [Wilmington, Delaware] Evening Journal (June 12, 1889):

NEW YORK, June 12.—J. J. Maroney and Charles McDonald, of this city, implicated in the murder of Dr. Cronin, have been arrested. The two men were taken to police headquarters and put in the celebrated cell No. 6, which has held more famous criminals than any other room in the country. They were brought in later before Inspector Byrnes and put through the "third degree" but nothing of any consequence was obtained from them.

A detailed description of how Inspector Byrnes applied the "third degree" in a particular criminal investigation appears in "The Third Degree: How Inspector Byrnes Secured Two Important Confessions: Modern Torture Chamber: Shrewd Devices of New York' Famous Detective: Why Jones Confessed His Guilt," in the Pittsburgh [Pennsylvania] Dispatch (September 22, 1889).

Conclusions

The earliest of these matches—from February 1883—attributes the term specifically to Inspector Byrnes, who uses the longer phrase "the third degree of initiation." This seems almost certainly to be a jocular allusion to the initiation rituals of various secret clubs of the nineteenth century.

Newspaper accounts of Inspector Byrnes and his interrogation method begin to appear outside the New York City area by the second half of 1889, as we see in newspaper articles from Delaware in June 1889 and from western Pennsylvania in September 1889.But these come after multiple mentions of the expression in New York City newspapers over the course of six years.

This appears to be a rather rare case in which the paper trail for a fairly old slang term leads to a particular person who may very well be responsible for coining the term.

The alternative suggestion (in Daniel's answer, citing Wikipedia) that "third degree" is attributable to Richard H. Sylvester of the Washington, D.C., police department is undercut by the fact that Sylvester didn't become the district's chief of police until July 1898, long after Byrnes began using the term "third degree" in the context of interrogation. In February 1883, Sylvester was 23 years old and about to start working for the Washington Metropolitan Police Department as chief clerk.