If a fever becomes too high, like 42.22 °C, you can die. Is it possible to put the patient in an ice bath to cool the fever down before that point and save their life?
In "A Journal of the Plague Year", Daniel Defoe writes of a febrile patient who cures himself of the plague by swimming in a river:
I heard of one infected creature who, running out of his bed in his shirt in the anguish and agony of his swellings, of which he had three upon him, got his shoes on and went to put on his coat; but the nurse resisting, and snatching the coat from him, he threw her down, ran over her, ran downstairs and into the street, directly to the Thames in his shirt; the nurse running after him, and calling to the watch to stop him; but the watchman, frighted at the man, and afraid to touch him, let him go on; upon which he ran down to the Stillyard stairs, threw away his shirt, and plunged into the Thames, and, being a good swimmer, swam quite over the river; and the tide being coming in, as they call it (that is, running westward) he reached the land not till he came about the Falcon stairs, where landing, and finding no people there, it being in the night, he ran about the streets there, naked as he was, for a good while, when, it being by that time high water, he takes the river again, and swam back to the Stillyard, landed, ran up the streets again to his own house, knocking at the door, went up the stairs and into his bed again; and that this terrible experiment cured him of the plague, that is to say, that the violent motion of his arms and legs stretched the parts where the swellings he had upon him were, that is to say, under his arms and his groin, and caused them to ripen and break; and that the cold of the water abated the fever in his blood.
Defoe's work is fictional, but presumably it is based on real anecdotes.
I'm still trying to track down references, but I also recall reading about indigenous tribes treating cases of the 1918 "Spanish flu" by submerging the sufferer up to his neck in a river. The cases were described in two separate books, one discussing South African responses to the pandemic, the other, those of New Zealand. I recall that in both cases the practice was condemned by colonial medical authorities. (For a South African reference, see Howard Phillips, "Black October", p. 170)
Here is an account by an army doctor who was one of the first victims of the "Hong Kong" flu of 1968, who caught it from a returning Vietnam veteran. There is no mention of an ice bath, but he says that the staff who treated him ran out of ice and had to request more from local restaurants.
I am not an expert, but I believe that Western medicine currently teaches that fevers have an adaptive purpose and should be allowed to "run their course", while Traditional Chinese Medicine acknowledges this but also identifies a category of illnesses where the high temperatures are harmful to the patient and should be treated with cooling medicines. In other words, the more nuanced view is that most or all contagious diseases may involve some kind of fever as part of the body's immune response, which is usually beneficial, except in cases of "high fever" where it is harmful. According to this theory, using an ice bath would be beneficial in certain types of fever.
For a historical background, the "Father of English Medicine" Thomas Sydenham is associated with early advocacy of the use of "cooling medicines" such as cowslips and laudanum, as well as bleeding, in the cure of fevers. I have spoken with modern ER doctors who will administer morphine, which lowers the body temperature, in the case of a high fever; and I have spoken with other ER doctors who have never heard of this practice but will prescribe ibuprofen to lower the body temperature. The practice of Sydenham's contemporaries was to treat fevers with stimulants, which Sydenham himself condemns. He writes (p. 149):
If bleeding cannot be resorted to [...] the heat of the distemper must by no means be increased. For this reason, the patient must be as much out of bed as he would be when in health, and (weather permitting) there must be no fire in the room. [...] Sometimes a patient has, with the extraordinary cunning of persons so afflicted, escaped the charge of his nurses while in a frenzy, escaped from bed, and exposed himself to the cold air, even during the night. Sometimes he has got cold water, either clandestinely or by earnest entreaty to the nurse, and drunk it off. In either case, by a happy error, a life that had been despaired of had been saved.
Prescribing a cold bath in certain cases seems consistent with Sydenham's views, but I wasn't able to find any place where he actually advocates doing so. One should note that Sydenham also warns that interfering with the course of a fever will tend to prolong it (p. 111) ("despumation" means "the act of discharging impurities from the body fluids"):
In either case, if you allow the effervescence (especially towards the end of a fever) to run its course naturally and in due form, if you take care that it is kept up in its proper vigour, the despumation will be completed within the aforesaid space of fourteen days or 336 hours. If, however, during the same period (that is, at the decline of the fever), you put any untimely check upon this same effervescence or fermentation, either by means of refrigerants or enemata, and if you curb it (as it were) in its natural career, you must not wonder if, when the order of Nature is disturbed, the disease becomes indefinitely protracted.