Reduction in transistor size has led to increase in transistor density allowing multiple cores to be placed on the same die; thus increasing the power dissipation of the chip. The heat dissipation by the cores may cause the chip temperatures to rise beyond a threshold limit causing it to malfunction. Dynamic Thermal Management (DTM) techniques address this issue by checking the rising temperature of the cores in the CMPs. Current techniques available for DTM use either Dynamic Frequency Scaling (DFS) or TM. The DFS based technique controls the chip temperature by reducing the cores operating frequency; however this may affect its performance. The technique of task rotation incurs the overheads of application migration. In this paper we propose a DTM technique that combines the benefits of both DFS and TM. The aim of the approach is to facilitate the efficient execution of high priority tasks. For this we allow other low priority tasks to sacrifice their performance to control the overall chip temperature. In particular, the high priority task is made to run at maximum allowable speed and, if needed, migrated to less heated cores while maintaining its performance. In this process, a low priority task runs at lower frequency to aid temperature reduction. Experimental analysis found that our approach reduces peak temperature of chip by 15.62 degree C with 0.24 percent performance (MIPS) degradation of high priority tasks compared to respective baseline. © 2018 IEEE.