While Softimage is running, %TEMP% is adjusted to point to a folder that looks like %TEMP%\XSI_Temp_11676:
LogMessage( XSIUtils.Environment("TEMP") ); // INFO : C:\Users\Stephen\AppData\Local\Temp\XSI_Temp_11676
11676 is the process identifier of the XSI.exe process. To show the process identifier (PID) in the Task Manager, click View > Select Columns and click the PID (Process Identifier) check box.
BTW, Process Explorer is handy for checking out the environment (and other properties) of running processes: