In some cases just increasing the temp will not kill ick, because there are different strains that tolerate higher temps.
Here in Panama ick thrives in ponds and small water bodies that easily hit 90'F and above.
The warmer water does helps speed up the multi phase ick life cycle making it easier to kill.
When the ick infection is visible on the fish, the treatment does not kill it. Ick has a hard cell membrane encased on the fish, and the fishes own slime coat also protects the protozoa.
It is when each spot releases hundreds of new young ick that the treatment becomes effective.
Those new young ick have not yet developed the hard cell membrane, and the salinity, and/or increased osmotic pressure from a chemical treatment like Nox-Ick make the young ick implode and you cure the disease.

If the young ick are not killed by osmotic pressure before resting in the substrate the hard cell membrane develops, and again in an inert state in the substrate they become immune to treatment.
They then become motile searching for a host, when motile the osmotic pressure of salt of chemicals is effective.
As an example I received a shipment where, probably due to shipping stress fish arrived covered in ick.

I did not raise temps, I did use 3 lbs of Morton water softener salt (NaCl) per 100 gallons of tank water.
Within 10 days, this is how those same fish turned out.

Another problem I find with raising the temp, is the point where each spot was on the fish, is an open wound area where secondary infection is possible, and higher temps often make pathogenic like Colomnaris bacteria more virulent, and more easily able to infect those open ick wounds. These secondary infections are often much harder and more expensiveto treat, especially because the fishes immune system may be weakened from the bout with ick.