Several long-lived nuclear isomer states with low energies are proposed to be used for searching the temporal variation of some fundamental constants. Orders of magnitude enhancements of the sensitivity to the fine structure constant, nucleon mass, meson masses and the strong interaction parameter are obtained in the transitions between these isomers and the ground states. The enhancement is mainly due to the low transition energy. The configurations of the states also influence the value of enhancement factor. There are both positive signs of the enhancement factors and negative ones in our results. We suggest to measure the ratio of transition frequencies in two nuclei with opposite signs of the enhancement factors. This could improve the sensitivity to the temporal variation of fundamental constants in experiment.