There are a few steps you must follow to allow Thunderbird to always show remote content of an email.
1) Navigate to and click on the menu button on the top right of your screen
2) Within the menu, select "Options" and then make your way to "Advanced" on the far right
3) On the general tab, click on the "Config editor"
4) In the window that appears, enter this into the search field (without quotes) "mailnews.message_display.disable_remote_image"
5) Double click the result that appears in the box below. The value should change to "False"
Close the window and you're done!
Hope this helped