heat and salt method has always worked for me on all sick fish i had ( not many sick fish throughout my fishkeeping though )
Raising the temperature on a tank of sick fish has nothing to do with sick fish in general. When the temperature is raised for ick, for example; it is due to how the heat affects the life cycle of the ick parasite specifically. Most other illness treatments that require raised heat, are also based on speeding up the life cycle of parasites. If the illness isn't parasitic, heat isn't likely to help, unless otherwise noted on medication instructions (though you won't use those, so it's a moot point).
Unfortunately, when it comes to fungal infections and many other illnesses, higher temperatures can make them worse. So by raising the temp, you're likely harming the fish with the mouth fungus.
While I agree that it's certainly important not to misdiagnose a fish illness and mistakenly treat with a medication that does more harm than good to a tank of fish that don't need it, some fish illnesses require chemical treatments whether you like adding chemicals to your tank or not. Ask anyone here who's tried to treat callamanus worms without Levamisole Hydrochloride or Fenbendazole based medications!
For the fish you claimed had ick, this isn't a super important point, as the salt & heat method does often work by itself. However, you mentioned putting all 4 fish in the same 10g tank, yet all 4 fish weren't suffering from the same illness. This means that if their conditions are contagious, you took 4 fish each suffering from a single illness, and gave them each a second illness to start their "healing process" with.
If I were you, I'd spend more time diagnosing the illnesses properly, then treat them accordingly. If you're not willing to do that, "rescuing" fish isn't likely to take place.
I'm going to stop now, and just say, "good luck".