Stainless steels are indeed protected by an extremely tightly-adherent, conformal coating of chromium oxide which forms the instant that the part is first exposed to air. This coating is optically transparent because of its thinness- only a few tens of atoms thick- but it protects the material underneath it because the rate at which oxygen can diffuse through it is extremely slow.
When it is heated as in your furnace, the diffusion rate is increased and so the creation of chrome oxide is "turned on" again until such time as the thickened oxide begins to choke off the diffusion of oxygen again, and the thickness of the oxide stabilizes.
This temperature-dependent, diffusion-limited and self-limiting pattern of behavior is called self-passivation and greatly complicates the dynamics of high-temperature corrosion.
As the oxide layer thickens, it begins to show optical interference effects between the front and back surfaces of the layer- and instead of appearing perfectly colorless, the film gets colored- first a light yellow which darkens into orange and then a brilliant blue as the film thickens. This color pattern then fades out and repeats; by counting these "fringes" you can accurately estimate the total thickness of the oxide.