Extractions of barrier heights of 6H and 4H-SiC Schottky diodes have been performed on structures with various gate metallization, using both capacitance-voltage (C-V) and current-voltage (I-V) measurements. The sum of the two barriers extracted by C-V measurements on both n-type and p-type materials is found to be higher than the band gap energy E-G, whereas the one extracted by I-V is less than E-G. However, above room temperature, temperature variations of barrier heights are in agreement with the variations of E-G. We have also computed theoretical I-V characteristics using a two-barrier height model. By taking account of temperature variations of a large number of parameters, e.g., the carrier mobility, free carrier concentration, and barrier height, we have achieved a good fit with experimental data. The model is shown to be valid for n-type Schottky diodes over a wide range of temperatures (from 100 to 500 K).