Abstract: The relationship between current and temperature is formulated analytically for n-GaN Schottky diodes based on the thermionic emission theory and the consideration of the experimental facts on the high thermal stability of the device. The energy-temperature transformation of the electrons in the conduction band of the device by application of the statistical mechanics principles (density of state and Fermi-Dirac distribution) resulted into an integral equation of current as a function of temperature for the device. The integral equation is solved analytically using power series expansion. The solution obtained is current-temperature formulation for GaN-Schottky diodes. This formulation will be a very useful tool in analysis and optimization of the GaN-Schottky diodes for applications at high temperatures. The second series of this study, which will come out very soon will establish the agreement between this formulation and the experimental results available on n-GaN Schottky diodes, using computer simulation technique.