High-quality optical resonators underlie many important applications ranging from optical frequency metrology, precision measurement, nonlinear/quantum photonics, to diverse sensing such as detecting single biomolecule, electromagnetic field, mechanical acceleration/rotation, among many others. All these applications rely essentially on the stability of optical resonances, which, however, is ultimately limited by the fundamental thermal fluctuations of the devices. The resulting thermo-refractive and thermo-elastic noises have been widely accepted for nearly two decades as the fundamental thermodynamic limit of an optical resonator, limiting its resonance uncertainty to a magnitude 10-12 at room temperature. Here we report a novel approach that is able to significantly improve the resonance stability of an optical resonator. We show that, in contrast to the common belief, the fundamental temperature fluctuations of a high-Q micro/nanoresonator can be suppressed remarkably by pure optical means without cooling the device temperature, which we term as temperature squeezing. An optical wave with only a fairly moderate power launched into the device is able to produce strong photothermal backaction that dramatically suppresses the spectral intensity of temperature fluctuations by five orders of magnitudes and squeezes the overall level (root-mean-square value) of temperature fluctuations by two orders of magnitude. The proposed approach is universally applicable to various micro/nanoresonator platforms and the optimal temperature squeezing can be achieved with an optical Q around 106-107 that is readily available in various current devices. The proposed photothermal temperature squeezing is expected to have profound impact on broad applications of high-Q cavities in sensing, metrology, and integrated nonlinear/quantum photonics.