In my case no, I also add everyone can save battery and memory just by avoiding installing Facebook app: it takes even 20% of your power. If you have Android, using Chrome and enabling Facebook notifications inside it will be more than enough, so that app is not needed.
Facebook app is really cool, but still eating resources in a phone, and this leads also to overheating.
If you use Chrome, I guess the situation will be much different.
However if you use other heavy apps, the problem will still persist. If your phone is still overheating, even without heavy apps opened, then I imagine there is a hardware problem in it.