The phrase your head’s on fire has been used to address a red-haired person.

The English antiquary and lexicographer Francis Grose (1731-1791) recorded this phrase in A Classical Dictionary of the Vulgar Tongue (London: S. Hooper, 1785):

Hyp, or hip, a mode of calling to one passing by; hip Michael ¹, your head’s on fire, a piece of vulgar wit to a red haired man.

¹ Michael, one of the commonest Irish male forenames, is perhaps used here because the Irish have been stereotyped as having red hair.

The following query was published in Local Notes, Queries, and Answers, published in the Leicester Chronicle and the Leicestershire Mercury (Leicester, Leicestershire, England) of Saturday 16^th January 1875:

QUERIES.

[65]. Local Characters.—“Bob! your head’s on fire,” was a name given to an eccentric blind fiddler who died some forty years ago, or rather walked into the river Soar and was drowned. It was he who first gave the Leicestershire Yeomanry Cavalry the nickname of “Butterfly shooters,” and “Bread and Cheese Tenters.” Can any of your readers of Notes and Queries give some of his songs and witty sayings?
H. Muggleton.

The answer to the above-quoted query was as follows in Local Notes, Queries, and Answers, published in the Leicester Chronicle and the Leicestershire Mercury (Leicester, Leicestershire, England) of Saturday 6^th February 1875:

ANSWERS.

[41, see query 65]. Blind Bob.—Allow me to correct your correspondent, H. Muggleston [sic]. “Blind Bob” was not a fiddler; he was a song-singer in public-houses […]. He was a stout man. He had red hair, a round face, and wore a hat very much on the back of his head, which gave him a singular appearance. He was called “Bob, your head’s on fire!” and “Hog’s puddings;” the first in consequence of having red hair, and the latter as it was reported he had stolen some black puddings: Whenever he appeared in the streets these epithets were fired after him, volley after volley, by the mischievous youths and roughs of the day; and he being very irritable, used to retaliate with some very low vulgar denunciations; and frequently, with the greatest fury, he would throw his stick at his assailants, which would cause crowds to assemble. […]
R. H.

The following story appeared in the column Facts and Fancies, published in The Knaresborough Post and Boroughbridge Herald (Knaresborough, Yorkshire, England) of Saturday 23^rd October 1897:

PLENTY OF WATER.

A young man was walking with some mates along the principal street of a small country town when, catching sight of a girl with bright red hair, and thinking to make himself look smart before his mates, he said:
“Excuse me, miss, your head’s on fire.”
The girl turned round and quietly replied:
“Oh, never mind; there’s water enough in yours to put it out.”
The young man did not wait to say good-night.

A variant of the story occurs in the account of the laying of the foundation stone of a Salvation Army hall in Bangor, published in the County Down Spectator and Ulster Standard (Bangor, County Down, Ireland) of Friday 21^st September 1906:

Lieutenant-Colonel Rowe, Provincial Commander for Ireland, said […] some criticisms were very fair, and deserved an answer, and the Army prided themselves in being able to give such criticisms a satisfactory answer. But other criticisms were unfair, and to those they hardly knew what to answer. Sometimes they were inclined to reply to them in the vein of the boy who when he was taunted for having red hair, by another boy who cried: “Hi, your head’s on fire,” retorted: “There is enough water in yours to put it out.” (Laughter.)

The following anecdote is from the column At the Pictures, by James Agate, published in The Tatler and Bystander (London, England) of Wednesday 29^th May 1946:

The author of Murder as a Fine Art ² was found one day in his drawing-room by his daughter with a writing-pad on his knees and his venerable locks blazing. “Daddy, dear,” said the affectionate child. “Your head’s on fire.” “Is it, darling?” said De Quincey. “Then put it out.” And he continued his writing.

² On Murder Considered as one of the Fine Arts (1827) is an essay by the English essayist and critic Thomas De Quincey (1785-1859).