We report the experimental observation and theoretical analysis of thermo-optic effects in high-Q on-chip lithium-niobate (LN) microdisks. We find that the resonance transmission dip of a LN microdisk was broadened or compressed when the wavelength of the input laser was tuned to the shorter or the longer wavelengths at a wavelength sweeping speed of 4.8 pm/s. When the laser wavelength was shifted with a fast rate (4.8 nm/s), the tendencies of the change in the shape of the transmission dip reverse completely. An oscillatory behavior in the transmission spectra was also observed when the laser wavelength was slowly shifted to the shorter wavelengths. The experimental results were successfully explained by using a theoretical mode considering for a fast thermo-optic effect of LN crystal and a slow heat dissipation process from the LN microdisk to the substrate and surroundings that leads to the reduction of the resonance wavelength through the deformation of the LN microdisk.