In recent years, cognitive radio (CR) has received a great attention due to the ability to improve the spectrum utilization. It allows the secondary user (SU) in the CR network to opportunistically access the licensed spectrum of the primary user (PU). For this end, quality of service (QoS) requirements for both the PU and the SU should be guaranteed at the same time. These QoSs can be respectively translated into the interference temperature at the primary receiver and the received signal- to-interference-plus-noise-ratio (SINR) of the secondary receiver. In such a CR network, a power control can increase the energy efficiency by keeping the transmission power of the SU as low as possible within the QoS requirements. In this paper, we propose an autonomous distributed power control scheme for CR networks that considers the QoS requirements of the PU and the SU simultaneously. Since the transmission power of each SU is constrained so that the interference temperature at the primary receiver caused by all SUs does not exceed the interference tolerance of the PU, the QoS requirement for the PU is always guaranteed. Through the simulation results, we demonstrate that the proposed scheme never exceed the interference tolerance of the PU.