For the relationship of wavelength change of narrow linewidth fiber laser and thermal tuning, experiments present that laser wavelength continuously change when the temperature changes, and the output power is undulating slightly, and mode hopping is not observed on the spectrometer.Self heterodyne of some temperature spots was measured, and the change of 3dB band width is smaller than 1kHz. Excellent spectrum properties and wavelength stability of fiber laser selected by fiber grating etalon are demonstrated.