Fully tested in Ubuntu 18.04 running the default Gnome desktop:
This works for me: https://itsfoss.com/install-nemo-file-manager-ubuntu/
In short, to use Nemo instead of Nautilus as your default file manager, including to manage desktop icons, do:
... [content intentionally deleted and moved to the link below]
UPDATE: My answer moved to here (How to set Nemo as the default file manager in Ubuntu 18.04?) since it pertains directly to using the nemo file manager instead of the default Nautilus, whereas the OP here is asking more about using Thunar.
If you need nemo, my link just above is perfect for you! Nemo is pretty similar to thunar in many ways too, so I highly recommend trying it out. Ubuntu's version of Nautilus, on the other hand, has removed many valuable features such as "Compact View", which I really miss. Therefore, I choose to use nemo.