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Accurate parameters of molecular hot-band transitions, i.e., those starting from vibrationally excited levels, are needed to accurately model high-temperature spectra in astrophysics and combustion, yet laboratory spectra measured at high temperatures are often unresolved and difficult to assign. Optical-optical double-resonance (OODR) spectroscopy allows the measurement and assignment of individual hot-band transitions from selectively pumped energy levels without the need to heat the sample. However, previous demonstrations lacked either sufficient resolution, spectral coverage, absorption sensitivity, or frequency accuracy. Here we demonstrate OODR spectroscopy using a cavity-enhanced frequency comb probe that combines all these advantages. We detect and assign sub-Doppler transitions in the spectral range of the 3ν₃ ← ν₃ resonance of methane with frequency precision and sensitivity more than an order of magnitude better than before. This technique will provide high-accuracy data about excited states of a wide range of molecules that is urgently needed for theoretical modeling of high-temperature data and cannot be obtained using other methods.