Personally, having just treated some new loaches for ich, I don't think I'd rely on temperature alone. It's useful for speeding up the lifecycle, but, reports of what temperature actually kills ich are varied. And it is known that there are heat resistant strains about. Old school fishkeepers have been using heat treatment for years and this is quoted on multiple sites, to me what this says is that resistance is bound to have evolved.
The numbers I've seen quoted is 30C to stop reproduction, so the theory is that after one lifecycle there is no parasites left. I'm a bit dubious about this. 32C supposedly kills the parasite, if treating with heat alone I'd want to get the tank up to this temperature, if your fish can cope. Just make sure you increase aeration, as long as you are getting plenty of oxygen into the water the heat probably won't be too much on an issue for a few days
Here is the thing though, if you try and treat with heat and it doesn't work what is the result, you've stressed this fish by raising the temperature, so they are more susceptible to ich and you've sped up the parasites life cycle giving them a chance to heavily infect the fish. What was initially a couple of parasites that were no more than a nuisance to the fish is now an attack that could be life threatening.
So my personal belief, and others will disagree, is that you want to increase the temperature along with treatment, so that the parasites reproduce faster but are also killed before they can reinfect the fish.
I'd treat with the King British, email the company if you are worried, chances are they will be very helpful. Plus I believe the KB contains quanine sulphate which from what I've been told should eliminate virtually all ich strains.
And most importantly, watch the fish after every change you make, if you add the treatment and the fish start acting funny, it's not a big deal, do a large water change and get it back out again. The other thing which is likely to be beneficial is not to use water conditioner if doing a water change where this is possible. If there is only chlorine in the water supply leave the water to sit in a container with an air stone running over night. If you do need to treat water try to treat only for what adding in. This way the water conditioner won't interfere with your medication.