Processing-in-memory (PIM) is regaining attention as a promising technology for improving energy efficiency of computing systems. As such, many recent studies on 3D stacking-based PIM have investigated techniques for effectively offloading computation from the host to the PIM. However, the thermal impacts of such offloading have not been fully explored. This paper provides an understanding of thermal constraints of PIM in 3D-stacked designs and techniques to effectively utilize PIM. In our experiments with a real Hybrid Memory Cube (HMC) prototype, we observe that compared to conventional DRAM, HMC reaches a significantly higher operating temperature, which causes thermal shutdowns with a passive cooling solution. In addition, we find that even with a commodity-server cooling solution, when in-memory processing is highly utilized, HMC fails to maintain the temperature of the memory dies within the normal operating range, which results in higher energy consumption and performance overhead. Thus, we propose CoolPIM, a collection of thermal-aware software-and hardware-based source throttling mechanisms that effectively utilize PIM by controlling the intensity of PIM offloading in runtime. Our evaluation results demonstrate that CoolPIM achieves up to 1.4X and 1.37X speedups compared to non-offloading and naive offloading scenarios.