To improve positioning accuracy of a magnetic head in hard disk drives (HDDs), a triple-stage-actuator system was developed with a thermal-positioning actuator for a magnetic-head-positioning system. This positioning system has three types of actuators: a voice coil motor (VCM), piezoelectric (PZT) actuators, and the thermal-positioning actuator. In this system, a magnetic head has a heater located in a horizontal direction of read/write elements as the thermal positioning actuator. By using this structure, the control system can move the position of read/write elements of the magnetic head in a horizontal direction with thermal expansion induced by the heater with an electric current. The thermal-positioning actuator is good for control in high frequency range because it has little adverse effect caused by mechanical resonances. As a result, the triple-stage-actuator system enable us to improve the positioning accuracy during a track-following control from conventional dual-actuator systems. However, the thermal-positioning actuator causes flying-height fluctuations of the magnetic head that may lead to worsening of magnetic recording performances. In HDDs, the magnetic head has another heater located in a vertical direction of read/write elements in order to control flying height of the read/write elements. This control system is called thermal flying-height control system. To compensate for the flying-height fluctuations of the magnetic heads caused by the thermal-positioning actuator, this paper presents a magnetic-head-positioning system that employs a feedforward control scheme on the thermal flying-height control system. Simulation results showed that the proposed method was able to compensate for the flying-height fluctuations during the track-following control by about 90 %.