Remember that iOS is built on the same Darwin kernel as its siblings MacOS, TVOS, and WatchOS uses virtual memory swapfiles, cache files, etc. The temporary disk space Tunein Radio is referring to is Storage space on the solid state drive in your iPhone.

WHERE IS THE STORAGE BEING USED?

While there is no Finder function per. se. there are at least a few ways of finding out how the storage on you iPhone is being used.
  1. Settings > General > Storage & iCloud Usage > Storage > Manage Storage will show how much storage is being used by each App and its associated data ranked from the biggest user to the smallest. Touching the App in this display will show a breakdown of how the storage is allocated within the App. While this does not show individual files it will give you an idea of where to start freeing up some storage.
  2. Connect your IPhone to iTunes on a computer via USB > click on the iPhone icon > select Summary under Settings will give you a graphic illustration of how the storage is allocated between Music, Movies, TV Shows, Boks, Audiobooks, and Tones (ringtones). Additionally by selecting each of those categories you can see the individual files for each of those categories and you can manage them there.
  3. iPhone Apps Within each app on the iPhone you will find the individual data files used by that app.

HOW TO FREE UP STORAGE

Now that you know where your storage is being used you know where to start freeing it up. There are two possibilities delete and move to iCloud.
  • PHOTOS Settings > Photos & Camera —
    • turn on iCloud Photo Library
    • turn on Optimize iPhone Storage
    • turn off keep normal photo in portrait and HDR modes
  • MUSIC Settings > Music
    • turn on iCloud Music Library
    • Turn on Optimize Storage
  • Take a hard look at your Apps including games an delete any that you are not using, you can always download the from the App Store at no charge if you decide to take them up again.
These changes will take a while to "settle" and you may have to invest 99¢ a month for additional iCloud disk space but if your storage usage is normal that should free up enough storage.

If we knew what it was we were doing, it wouldn't be called research, would it?

— Albert Einstein