If you don't see a temperature alert your iPhone is probably not malfunctioning. I don't remember the working range for temperature, but design specification is almost certainly higher than you expect. An important sales area for Apple is Middle East where outside temperatures are routinely above 40˚C and everything feels hot to touch. If they can work in Kuwait and Saudi heat then almost anywhere else in the world will be easy.
I suggest trying to get some clues which apps are the battery hogs, because they will be responsible for a lot of the heat generation. (Battery usage = power used = heat generated). A look at the battery usage statistics in Settings/Battery might be a good place to start, along with your impression of which apps seem to be most greedy. Hint: Some of the social media apps have attracted attention in the past for excessive battery usage, so they might be a good place to start looking.
Heat generation during charging is normal and expected as a consequence of basic physics if it simply gets warm. If it gets hot (too hot to hold, think like a coffee mug) then you might have a problem. Your observation of reduced heat above 80% charge is also expected because the charging sequence usually runs faster (more heat) when charge is lower then backs off as it approaches the final charge level. You might also be seeing the result of Optimized Charging, which can learn your usage pattern and try to reduce stress on the battery.