A high-power, wide-band, steady-state amplifier was developed as a part of research and development for ion cyclotron range of frequency (ICRF) heating in the Large Helical Device at the National Institute for Fusion Science. A double coaxial cavity was adopted to cover the wide frequency range of 25 to 100 MHz. An analysis of this cavity is compared with results of static tests, and good agreement is shown. In a high-power test, long-pulse operation of 5000 s at an output power of 1.6 MW, which is a world record for steady-state operation of an ICRF amplifier, has been achieved as a low-impedance-mode operation is adopted. Cooling of various elements of the amplifier is important in the steady-state operation. This paper reports how the steady-state operation is obtained through cooling. An analysis of heat removal in response to the temperature rise of a coaxial cable is also reported.