I don't raise the temp with ick, because that often provides a pathway for pathogenic bacteria to infect the lesions the icK create. And most bacteria thrive and grow even more virulent at temps above 80'F. Epistylis and Columnaris are a couple examples of bacteria that prefer heat, and take advantage of the lesions ick create in the fish skin.
Although I have used meds infused with Machite and similar toxic minerals at times, unless you substantially increase aeration when using them, they can (as said above) be problematic, and create anoxic enough conditions to kill certain species, especially if crowded in a QT tank.
And once 1 fish dies in a tank deteriorating water quality, others often follow, and are probably the cause of the high nitrates you found.
I use salt, at a concentration of 3 lbs per 100 gallons to cure ick, and it has always worked for me in past, and is about the least toxic option available compared to certain osmotic pressure increasing compounds (like the malachite, or formaldehyde in some fish meds).
The problem with heat, is that there are strains of ick that are resistant to it.
Here in Panama, the average temp of waters where I collect cichlids is 82'F, and I sometimes will net an individual that contains an ick parasite or 2, happily existing in those 80s+ water temps.
View attachment 1535957View attachment 1535958
The thermometer above was used to take the water temp of the Mamoni river
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