If you keep a very clean tank, the possibility of a healthy fish in pure water conditions, being infected by a parasite or anything else, is very remote. I've kept tanks for many years and never had a problem with infections or parasites. This is because I make sure and remove and replace most of the tank water every week. Harmful parasites and similar things are unable to live and reproduce in pure water conditions.
Heat is a poor remedy for Ich. It increases the metabolism of the parasite, yes. But, it does the same to your fish. A higher metabolism, means the fish poop more. Not what you want when you need to clean up the tank water. Use large, frequent water changes and a teaspoon or two of standard aquarium salt to every five gallons of new, treated tap water. Do a good job of vacuuming the bottom material when you change the water. I'd change half the water twice weekly, vacuum the bottom and use the salt until you see improvement in the health of the fish.
"Fear not, my young apprentice. Just change the tank water."