An X-ray radiation source with approximately constant radiation temperature is realized by irradiating golden hohlraum with a shaped laser pulse. A simple theoretical model based on power balance is used to design the shape of the drive laser pulse. Experiments are carried out on the Shenguang III prototype laser facility, and the experimental results are presented for radiation sources with the flat-top lasting about 2.5 ns at two different peak temperatures of about 150 eV and 170 eV, respectively, including the time histories of the temperatures, the shapes of the drive laser pulses and the time integrated radiation spectra. The validity of the model and possible improvements are discussed.