High resistivity CdZnTe is a very promising material for X-ray detection at room temperature or slightly below. Cooling a Cd0.8Zn0.2Te crystal down to -30-degrees-C reduces the leakage current to the picoamp level, which enables the use of low-noise pulsed optical feedback instead of noisier resistive feedback preamplifiers. Also, longer shaping time constants at the linear amplifier can be used for the optimum resolution. We have obtained resolutions of 240 eV (FWHM) for the 5.9-keV Fe-55 line at -40-degrees-C and of 282 eV at -30-degrees-C. The Fano factor for the material at -40-degrees-C was calculated to be 0.14. These results compare well with the results obtained with peltier-cooled HgI2 detectors.