<p>This study is devoted to free vibration analysis of cracked temperature-dependent functionally graded beams under nonlinear temperature rise. First, governing equations for vibration of temperature-dependent beam structures are established using the power law of material gradation, the double spring model of open transverse crack and Timoshenko beam theory. The constructed analytical model of the beams allows thoroughly investigating the crack compliance (local flexibility) in dependence upon material gradation index, crack depth and temperature. Second, using exact analytical method, general solution for free vibration of the beams with single crack is conducted and used for examining variation of the beam’s natural frequencies along crack position and depth, material gradient index and temperature rise of different distributions. Numerical results demonstrate that crack compliance increases with crack depth and decreases for growing material gradient index and temperature rise. Moreover, it is revealed also that temperature rise has a significant effect on either natural frequencies or their sensitivity to the crack. The theoretical development has been validated by comparison of the numerical results computed hereby with those published earlier in the literature.</p>