Unity failing to open projects on other drive

I have an issue that is only prevalent on my office machine. If I try to open a project that is hosted on my D:/ drive then I get two errors along the lines of this:

 Microsoft (R) Visual C# Compiler version 2.9.1.65535 (9d34608e)
 Copyright (C) Microsoft Corporation. All rights reserved.
 error CS2011: Error opening response file 'C:\Temp/UnityTempFile-f452cacae838d9b4c940401c33787d06'
 warning CS2008: No source files specified.
 error CS1562: Outputs without source must have the /out option specified

The project becomes completely unusable in this state. Even creating an empty project from scratch in the D drive causes this error.

I reckon it must be something to do with my drive setup or permissions, as this issue doesn't happen with my home machine. Has anyone had anything similar and found a resolution?

See a previous forum post discussing this issue from the beginning of the year.

Note, the Temp files it says it can't find are located within the Temp folder of the project itself.