hold on, your redoing your tank because of a fish? what other reasons?
your idea sounds ok, i dunno how long the fish are gonna be in a non-heated bucket, you might just wanna buy a hospital tank and store them in. then i would refill what gallons you have in your main tank, and turn the water up, and because you wont have any fish in it, turn the heater way up, past 90 at least. the ich, as us fw
people do it, is let the tank sit on a high temp for 2 weeks.
a flaw would be, that if your fish could already have ich in the bucket with them, so the only way would be also to use ich treatment (careful, i know it killed 2 dwarf gouramis in 2 days) and sw
fish are a lot more sensitive, so maybe turning the water up to 87 (we fw
people treat ich at 87, i dunno how sw
fish would react)