The Kramers-Kronig transforms (KK) constitute a powerful tool to validate experimental data. The present study is implemented for Bi2O3 thin films deposited by thermal vacuum evaporation at different temperatures of the glass substrates. Since the extraordinary properties of this fabric allow us to consider particular analytical approach as it was previously shown, the reflectance properties of Bi2O3 as a function of temperature could be studied.The novelty of this article is the studying of a global effective analytical representation, based on polynomial functions, in order to obtain a general model that includes temperature dependence of the optical properties, using the Kramers-Kronig transformation type. In the mathematical expressions, were included mix combined term in order to avoid the effects of Runge phenomenon. As a case study was chosen Bi2O3 - a substance less studied in literature. In the last part are the presented and commented the results obtained for a series of eight studied models.