Of American-English origin, the colloquial phrase hot under, or in, the collar means extremely exasperated or angry.
The earliest instance that I have found is from The Chicago Tribune (Chicago, Illinois) of 8th July 1869, which published a report, dated 27th June, from its special correspondent in Salt Lake City:
Seward¹ and party came, to whom the Mormons were especially attentive, and not without the desired effect. For, in response to a Mormon serenade, “the old man eloquent²” imprecated the blessings of Heaven on his entertainers, which caused the Gentiles³ of the city to wax hot in the collar, and they got up a serenade for next evening, a party of Chicago ladies and gentlemen having arrived meanwhile.
¹ William Henry Seward (1801-72), Republican politician, successively Governor of New York, Senator and Secretary of State
² the Old Man Eloquent: a nickname for John Quincy Adams (1767-1848), 6th president of the USA (1825-29), here apparently applied to William Henry Seward (perhaps derisively, as he was renowned for speaking monotonously)
³ a Gentile: one outside the Mormon community
I have found a literal use of hot under the collar in The Elko Independent (Elko, Nevada) of 18th June 1870, which published a description of the Ruby Cave, near Camp Ruby, a fort built in Nevada in 1862 by the United States Army (commissary seems to denote an alcoholic drink provided by the commissary, that is, the officer in charge of the supply of food):
The Ruby Cave.
It can only be explored by means of a boat. It is one half mile in length by from twenty to fifty feet in width. The water is from ten to twenty feet in depth. It was once the favorite resort of parties from Camp Ruby, and many gallons of “commisary” [sic] that have been charged upon the commissary as having been issued to extra duty men, or lost by evaporation, have been drank [sic] while exploring that cave. I once heard of a stage man who after imbibing rather freely swam out with his boots on. The water was rather cool, but as he was hot under the collar he did not catch cold. I think I have also heard of a man who at that time wore brass buttons, who did likewise.
advertisement for Food City
Kingsport News (Kingsport, Tennessee)
Wednesday 24th September 1975
Are Today’s Food Prices Getting You…
“HOT UNDER THE COLLAR”?