Performance of whispering gallery mode resonators can be compromised by resonance wavelength fluctuations. Here, we employ a silica microsphere coupled with a pair of head-on, single-ended tapers to show that the resonator by itself can latch onto a specific mode when the wavelength of a high-power laser changes over many resonance peak widths in both directions. We also show that, at high power of pump-in laser, the resonator can self-tune its resonance to a fixed wavelength when the resonator temperature changes or the gas flow surrounding the resonator changes, but the resonance is easily lost when the power is low.