Transmit temporary file structure Transmit normally stores files at:
~/Users/esemrow/Library/Caches/Cleanup At Startup/Transmit/300C3B29-9684-443B-9784-9316236D5795/index.php

Is there a way to have it mimic the remote file structure?
e.g. ~/Users/esemrow/Library/Caches/Cleanup At Startup/Transmit/domain.com/www/site/public_html/my_folder/index.php
Not as far as I know currently, no. You can talk to the developers on Twitter: @panic