A photonic resonator analyzer characterizes a photonic resonator and incudes a light source that provides a probe light; a photonic resonator that receives the probe light and produces product light; an optical detector that receives the product light and produces a product signal; a mode analyzer that receives the product signal and produces a resonator spectrum; and a spectral analyzer that receives the resonator spectrum, performs regression by fitting a non-parametric model to the resonator spectrum, and produces a thermal response function of the photonic resonator from fitting the non-parametric model to the resonator spectrum to characterize the photonic resonator.