Problem:  

RDP users cannot install Chrome extensions from the Chrome Web Store.

Errors:

• Could not install package
• COULD_NOT_GET_TEMP_DIRECTORY

Figure 1:  Chrome Temp Directory Error

Solution:

1. User logs onto RDP.  User does not open Chrome.
2. Admin creates a new directory on the system drive.  This new directory holds user Chrome AppData.  For example:  c:\\mkdir c:\Temp\RDP\
3. Move user’s Chrome AppData to the new directory.  For example:
   c:\move "c:\users\stevenjordan\AppData\Local\Google\Chrome" "c:\temp\RDP\stevenjordan\"
4. Delete original folder if necessary. 
5. Create new symbolic junction where the old data was located.  This junction links to the new location:

c:\mklink /j c:\users\stevenjordan\AppData\Local\Google\Chrome\
"c:\temp\RDP\stevenjordan\Chrome\"

Junction created for c:\users\smjordan\AppData\Local\Google\Chrome\
=== c:\temp\RDP\stevenjordan\Chrome\

Figure 2:  New Symbolic Junction for Chrome extension.

Analysis:

Chrome extensions reference DOS device paths.  Let's consider how dynamic profile disks use symbolic junctions that point to different disks:

c:\Users  dir 
02/23/2018  11:29 AM  bgates {\??\Volume{a5ae22c7-18b8-11e8-968e-00145de79140}

The junction link causes the problem.  Ironically, a second junction link fixes this issue:

c:\Users\bgates\AppData\Local\Google dir
 
 Directory of c:\Users\bgates\AppData\Local\Google

02/20/2018  10:58 AM   DIR
02/20/2018  10:58 AM   DIR
02/20/2018  10:58 AM   JUNCTION  Chrome c:\temp\RDP\bgates\Chrome
09/16/2015  07:46 AM   DIR       Chrome Cleanup Tool
05/14/2014  06:09 AM   DIR       CrashReports
03/11/2014  04:26 PM   DIR       Google Talk
12/04/2017  02:27 AM   DIR       Software Reporter Tool

0 File(s)              0 bytes
7 Dir(s)  36,942,458,880 bytes free

Note how the new junction link points to the system drive.

Additional Thoughts:

This solution is implemented on a per-user basis.  It does not universally "fix" Chrome extensions for all RDP users.  Nonetheless, it may be a good fit because it narrows the scope of untrusted applications.

Alternatively, use Group Policy to change user environmental variables:

Group Policy
→ Computer Configuration
      → Administrative Templates
         → System
            → Group Policy
               → Configure user Group Policy loopback processing mode:
                       Enabled:  On
                       Mode:  Merge

   → User Configuration
      → Windows Settings
         → Preferences
            → Environment (right-click) → New
               → New Environment Properties:
                      Action:  Update
                      User Variable=Check
                      Name=Temp
                      Value=c:\Temp\RDP\%USERNAME%
              → Environment (right-click) → New
                      Action:  Update
                      User Variable=Check
                      Name=TMP
                      Value=c:\Temp\RDP\%USERNAME%

This change has a wider-scoping impact.  It affects all related AppData programs -not just Chrome.  It impacts all RDP users (without GP filtering).  Avoid the system drive if possible -use a secondary disk instead.  In addition, loopback processing applies user configurations to computer objects (i.e., RDP servers).

That's It!

References:
https://blogs.technet.microsoft.com/grouppolicy/2009/05/13/environment-variables-in-gp-preferences/
https://devtidbits.com/2009/09/07/windows-file-junctions-symbolic-links-and-hard-links/
https://blogs.msdn.microsoft.com/jeremykuhne/2016/04/21/path-format-overview/
https://blog.brankovucinec.com/2017/01/09/users-cant-install-google-chrome-extensions-on-rds-farm/