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Whispering-gallery-mode (WGM) microcavities strongly enhance nonlinear optical processes like optical frequency comb (OFC), Raman scattering, and optomechanics, which nowadays enable cutting-edge applications in microwave synthesis, optical sensing spectroscopy, and integrated photonics. Yet, tunability of their resonances, mostly via coarse and complicated mechanisms through temperature, electrical, or mechanical means, still poses a major challenge for precision applications as above. Here, we introduce a passive scheme to finely tune resonances of WGMs at MHz precision with an external probe. Such a probe remotely transfers heat through a gap from an optical microcavity, effectively tuning its resonances by thermal-optic nonlinearity. Moreover, we explore this unique technique in microcavity nonlinear optics, demonstrating the generation of a tunable OFC and backward stimulated Brillouin scattering with variable beating frequencies. This technique addresses the core problem of WGM microcavity's fine-tuning, paving the way for important applications like spectroscopy and frequency synthesis. [ABSTRACT FROM AUTHOR]