Question: When running a web application project, at seemingly random times a page may fail with a CS0433 error: type exists in multiple DLL's. The DLL's are all generated DLL's residing in the "Temporary ASP.NET Files" directory.

Answer: 
In my case, the problem was solved when I edited a Designer.cs file that still had the duplicated class name. for some reason, when i renamed the class "logout" to "logout2", in the designer file it was not automatically changed, and was still "logout", and this class name already existed in a precompiled dll in my project (that belongs to a third party web app that I work with and develop around of).
For me this happened when I had my PrecompiledWeb/Publish location set to the current directory which was where the site's root folder was too.

My Web Site was then seeing the publish folder as part of the project when compiling/building and then finding duplicates in that manner.

i.e. Don't put the published/precompiled version of your site in your site's code folders.