The easiest way to change where ACR puts temporary files is to edit the environment variables and change TEMP & TMP to point somewhere else.
By default these are both %USERPROFILE%\AppData\Local\Temp
For example, if I do this:
C:\> SET TEMP=Z:\TMP
C:\> SET TMP=Z:\TMP
C:\> MKDIR Z:\TMP
C:\> "C:\Program Files\Adobe\Adobe Bridge CC\bridge.exe"
Then ACR will get run and put the temporary files it creates in Z:\TMP rather than on the C:\ drive.
While I can put all of the above in a BAT file to launch Adobe Bridge with, it would be nice to be able to set this inside the application so that when it gets launched from a menu, "it just works." I suspect that the same also holds true for LR.
The next goal is to try using a shortcut with something like this:
C:\Windows\System32\cmd.exe /c 'set TMP=Z:\TMP && SET TEMP=Z:\TMP;"C:\Program Files\Adobe\Adobe Bridge CC" && start bridge.exe'