When a car is being designed, there comes a moment when the sketches are turned into a tangible model. Nowadays this is done with clay or a synthetic derivative thereof. In the past, this was done in wood and plaster and that happened, certainly for Italian car manufacturers, often at specialized companies. One such company was "Alfredo Stola Modelli Dimostrativi In Legno Per Fonderia E Carrozzeria". They started around 1920 with wooden models for Lancia and later Fiat and Pininfarina became frequent customers. Find out more about their history HERE.
On their site you'll find these pictures, important moments in the development of the Fiat 850's (unfortunately I haven't found anything of the Berlina yet):
Of course they wanted to make sure it was a nice car:
Yes, as a support bus for their cycling team.