Fast charging and wireless charging are both detrimental to battery longevity.
I can't speak to wireless charging, as I haven't done any research on it or used it myself. I have looked into wired charging through various sources (namely Battery University) and fast charging on phones is not too fast for standard Lipo batteries. If you're familiar with C ratings on batteries, Lipos can handle a 1C charge without issue. Most phones don't cross that, even with fast/quick charging (there may be one or two outliers, but I'm speaking in general). I do commonly see 2- 5C charging in some hobby Lipos, and those batteries are designed for it.
Now if you are using the phone, that can possibly add to the heat that can damage a battery, but that's why phones throttle their charge rates when this happens. It's to protect them. If your phone is getting that hot, then it's not the charging rate killing it. Heck, in some cases it could not be charging at all.