Windows 7: \Windows\Temp

It's actually pretty difficult. You can use the setx command to set persistent environment variables for other users, but this won't work for NetworkService, because the service accounts have no passwords (so your credentials will always be rejected).

The only way that I know of to do this is using the task scheduler:

1. Set up a task to run as the user "network service".
2. Leave the triggers empty.
3. For the action, have it run cmd.exe with the parameters /c setx temp [target].
4. Run the task manually.
5. Delete the task.

This will work to set a persistent environment variable for the NetworkService user. As to whether this will successfully work to relocate the temporary files for that user, or whether it will cause any unpredictable side-effects, I can't say for certain. You may need to reboot to verify if it's putting the temp files where you want them.

You can verify that the environment variable has been changed for the correct user by using the environment command within WMIC.

Some programs keep important files in there, surprisingly. If you are interested in freeing some space I'd advise to only delete the files excluding those that were created in the last 24h or so, or the ones you know for sure aren't used by other programs, such as old installers from software you downloaded, etc. You can use software such as CCleaner to do that.

The answers to this question provide ways to do this clean-up safely and automatically.