Today I decided to update my Kobo Touch C to FW 3.13.1 via wifi by using KSM's "kobo FW update.msh". Unfortunately, the update process did never finish, white screen and green blinking led for ages. I finally triggered a factory reset.
Since there are several ways to set up one's device, I describe how I did it for further reference in form of a how-to-do.
On a side note: I tried again to install 3.13.1 via wifi by "kobo FW update.msh". This time it worked without any problem. Why it did not work the first time, I do not know. Presumably, the cause was something in the "history" of the device.