In this work, the thermal characterization of continuously pumped passively Q-switched laser is quantitatively represented. The system under investigation is end-pumped Yb:YAG passively Q-switched by Cr⁴⁺:YAG as saturable absorber. The rate equations describing the dynamics of laser action are numerically solved simultaneously with the temperature conductivity heat equation to depict the transient temperature distribution. The study has been performed in the cylindrical coordinates to characterize the temperature distribution in the axial and radial directions. The thermal transient time in both directions as well as the thermal focal length are calculated. The temporal behavior of the temperature distribution has been illustrated in a 3-dimensional diagram.