On my machine, TEMP environment variable is defined as 'D:\Temp'.
When I run msys, 'echo $TEMP' gives '/tmp', and 'msysmnt' shows that D:\Temp is mounted on /tmp. That's fine.
When I run an external application from msys, the TEMP variable is modified to 'D:/Temp'.
To reproduce: Run msys, from it, run cmd /c "echo %TEMP%"