Three-dimensional integrated circuits (3D ICs) provide an attractive solution for improving circuit performance. Such solutions must be embedded in an electrothermally-conscious design methodology, since 3D ICs generate a significant amount of heat per unit volume. In this paper, we propose a temperature-aware 3D global routing algorithm with insertion of "thermal vias" and "thermal wires" to lower the effective thermal resistance of the material, thereby reducing chip temperature. Since thermal vias and thermal wires take up lateral routing space, our algorithm utilizes sensitivity analysis to judiciously allocate their usage, and iteratively resolve contention between routing and thermal vias and thermal wires. Experimental results show that our routing algorithm can effectively reduce the peak temperature and alleviate routing congestion.