Explain what you mean by "Where does the modem fit in"..
If a device runs hot, it could be any number of things. If you overclocked the phone, then it could be causing it, but there are many things to check.
I have mine overclocked to 1.4ghz at the moment. In order to make sure I don't have any problems with heat (which at 1.4ghz its not likely), I keep things running minimal. My screen stays at 30% inside, and no higher then 70% outside. My background data is off until I need to use Play Store, then I turn it off when I'm done. I don't store or leave the device in sunlight, or in a car. And I make sure to turn off any app that I don't need to be constantly running in the app manager.
For the ram clearing, I use the Task Manager widget on one of my desktops.
For cache cleaning, I use SD Maid by DARKEN from the app store. It works wonders and is lightweight. I have never used Android Tuner, so I'm not familiar with its function.
My current setup is: OS (Xperion ROM), removed excessive bloat, Overclocked Kernel (Freedom Kernel), OC to 1.4 this
I have no problems with anything