Pyrolysis conditions directly influence biochar properties and, consequently, influence the potential use of biochar. In this study, we evaluated the effects of different pyrolysis temperatures (450, 550, 650, 750, 850, and 950 °C) on the hydrogen potential, electrical conductivity, ash content, yield, volatile matter content, elemental analysis, Fourier-transform infrared spectroscopy results, X-ray diffraction results, scanning electron microscopy results, specific surface area, and micropore volume of eucalyptus wood-derived biochar. The degree of linear association between pyrolysis temperatures and biochar properties was examined using the Pearson correlation coefficient. The results showed a positive correlation of the pyrolysis temperature with the hydrogen potential value, electrical conductivity, and elemental carbon. There was a negative correlation of the pyrolysis temperature with the yield, volatile matter content, elemental oxygen, elemental hydrogen, surface area, aromaticity, hydrophilicity, and polarity indexes. The Fourier-transform infrared spectroscopy data indicated an increase in aromaticity and a decrease in the polarity of high-temperature biochar. The increased pyrolysis temperature caused the loss of cellulose and crystalline mineral components, as indicated by X-ray diffraction analysis and scanning electron microscopy images. These results indicated that changing the pyrolysis temperature enables the production of biochar from the same raw material with a wide range of physicochemical properties, which allows its use in various types of agricultural and environmental activities.