On linux it works more or less the same way, a little program (that Werner also programmed
) called freecad-thumbnailer extracts the .png thumbnail stored in the .fcstd file. That thumbnailer is registered somewhere so the file managers know when to use it.
Indeed there are a lot of distros, desktops and file managers around, but there is also a *kind of* standard called freedesktop.org, which at least all the major desktop systems such as gnome, kde and lxde follow (more or less). For example, it defines the arguments that the thumbnailer program must take. As far as I saw, Werner's thumbnailer follows all the freedesktop standards.
The problem most probably lies in the way that thumbnailer is registered... For gnome/nautilus, it's an entry in gconf (the gnome's "registry" (never understood how/why a linux desktop must have a registry, but...)), for thunar it's a .desktop file in /usr/share/thumbnailers, and for kde I don't know.
That "registration" simply specifies a thumbnailer program to be called on certain MIME types. So for nautilus, the best way to check is to open gconf-editor and navigate to Desktop>Gnome>Thumbnailers and see if the freecad one is there. AFAIK freecad correctly registers its thumbnailer there on installation (but I don't use gnome so I cannot check here)
For Thunar, it seems something changed recently and several of my thumbnailers don't work anymore, so probably nothing to do with freecad itself...