Just because the most recent answer is 5 years old, what had to be done in our environment was to delete the app, app pool and recreate them.
We evidently have some security under the hood with recent changes to it.
Doing this re-created a folder in Temporary ASP Net Files with all the correct permissions. Why the one site I happened to just get from source control, rebuild, etc. failed this way, no idea. 2 others recently set up where Get Latest Version was downloaded, rebuilt, etc. they just worked.
But ripping out the app, app pool and just recreating them with the same IIS permissions as the 2 other known working sites recreated all the needed objects and now it all works.