Is this paper we mainly investigate the effects of the temperature and Josephson energy on teleportation of one qubit state in both the standard and the non-standard protocols as well as the partial teleportation of an entangled state under the standard protocol via two identical superconducting charge qubits in thermal equilibrium as the teleportation channel, and give the analytical expression of the average fidelity. Our results show that the teleportation of one qubit state in non-standard protocol and the partial teleportation of entanglement in standard protocol can be almost perfect, indicating that quantum teleportation, with using superconducting charge qubits in thermal equilibrium as a quantum channel, is feasible in theory.