You decide the task of determining the properties of the oxide under standard conditions (0-100 0 C, air)? If so, then why do you need other conditions?
In some literature, mentioned that air or nitrogen used as atmosphere to reduce oxidation and reduction. That's why i am asked the question in this forum.
As Fe2O3 can transform to Fe3O4 or as the compound can loos O2 in the course of the heating, I would run TGA under N2.
Air or Oxygen atmosphere is suggested for the cases that there are organic and inorganic phases and one needs to determine the weight ratio of each phases. In those cases O2 atmosphere is used as under O2 atmosphere the combustion is complete.
N2 atmosphere is used when one needs to determine mechanism of a reaction for example to determine the activation energy.
The experimental conditions depend on the aim of your work. Inert atmosphere (N2) is used when you are interested to mechanism of a chemical reaction. Air or oxygen if you want to induce an oxidation and a formation of specific phases. In your case it seems that N2 is the preferred choice. Also the temperature range of interest could be varied depending of your aim.