The emission of resonant radiation from temporal solitary waves—also known as dispersive wave generation—allows efficient energy transfer to far‐distant spectral domains. This coherent radiation can deliver large spectral densities at selected wavelengths once control over the individual soliton is achieved. Here, the concepts of few‐mode operation and local temperature tuning are combined for precise steering of cascaded dispersive wave generation in liquid‐core optical fibers. By exciting higher‐order TM and TE modes with femtosecond pulses at 1600 nm, the generation of two dispersive waves tunable by up to 33 nm K−1 through adjusting a selected part of the waveguide is observed. Sophisticated soliton‐driven nonlinear dynamics arising from thermally transitioning from anomalous to all‐normal dispersion with temperature changes of only a few Kelvin have been found, including soliton steering, soliton breakdown, and soliton post‐fission tuning. All experimental results are verified by nonlinear simulations and semi‐analytic phase‐matching calculations, overall providing a cost‐effective and practical toolbox for discovering unexplored states of light as well as for developing dynamically tunable broadband light sources.