Temps will kill it. Not having a host will kill it. Salt will kill it. Granted, the temps high enough to kill it will also kill the fish. So...
The important thing is that ich does NOT occur in all tanks. Ich can be introduced into a tank, and due to it's life cycle, be there for months without being noticed because it is only visible to us a) at a specific stage in it's life and b) when fish infestations are very heavy. Most of the time, the parasite attaches to the gills, where it's hidden. That's how it gets imported--people can't see the parasites, and don't quarantine. So, one cyst on a gill comes in. At this point, it's well protected from most medications, since that cyst protects it. It drops off, hangs out in the substrate, then hatches into the free swimming stage. While in the substrate, it's safe from everything but manual removal. Once it hatches, it's susceptible to salt or other medications. It's looking for a host--and by 'it', I mean hundreds of them. In the wild, the parasite probably won't find a host. In our tanks, they will. They target the gills of the fish, burrow in, and start eating. Now, the immune system of the fish attacks it, and if it were just ONE parasite, would probably be ok. The fish would be irritated for a while, but survive. In tanks, each fish is likely going to pick up more than one--lots and lots. Some fish have thicker slime coats, so are resistant to the ich, but even they can be overwhelmed. So now, the fish protects the parasite from most medications--internal meds from treated food will help, but most additions to the water won't. The parasite noms along, before encysting into the familiar white crystal on the surface of the fish.
This whole process can take 30 days at cooler temps. The parasite can't control how fast it develops, that's based on the temp. So, raising the temp forces it to go faster, meaning it gets to a treatable stage faster. Temps higher than 86 *may* kill it, but not always, but it will shorten the life cycle to 2 weeks. Temps higher than 86 aren't really safe for most fish. Salt does 2 things: fish will produce a thicker slime coat, making it harder for the parasite to reinfect; salinity kills the free swimming stage. That's why it's important to treat past the last visible spot.