Enhanced absorption is obtained in a hybrid nanostructure composed of graphene and one-dimensional photonic crystal as a cavity in the visible wavelength range thanks to the localized electric field around the defect layers. The temperature-induced wavelength shift is revealed in the absorption spectra in which the peak wavelength is red-shifted by increasing the temperature. This temperature dependence comes from the thermal expansion and thermo-optical effects in the constituent layers of the structure. Moreover, the absorption peaks can be adjusted by varying the incident angle. The results show that absorption is sensitive to TE/TM polarization and its peak values for the TE mode are higher than the TM case. Also, the peak wavelength is blue-shifted by increasing the incident angle for both polarizations. Finally, the possibility of tuning the absorption using the electro-optical response of graphene sheets is discussed in detail. We believe our study may be beneficial for designing tunable graphene-based temperature-sensitive absorbers.