This work presents the results of temperature-based control of supercontinuum generation in liquid-core step-index fibers. The key parameter adapted via temperature is the group velocity dispersion of the fiber modes, which determines the nonlinear pulse dynamics. Different soliton dynamics, e.g. fission, breathing, breakdown, and tunneling, are studied experimentally and numerically exciting higher-order modes in approximately 10 cm-long carbon disulfide-filled step-index fibers with ultrashort sub-40 fs pulses centered at a wavelength of 1.57 μm. By modifying the temperature of defined fiber sections, strong wavelength shifts of up to 33 nm/Kelvin are detected. The generated dispersive waves reach infrared wavelengths of up to 2.7 micrometers. The experimental results showing these strong thermo-spectral shifts are in good agreement with numerical simulations solving the nonlinear Schrödinger equation and corresponding phase matching calculations. The nonlinear simulations give further insights into the soliton dynamics taking place inside the fiber. In this way, the different soliton processes can be identified and precisely controlled via temperature. Parameters studies are conducted to learn about the optima and limits of the different soliton effects. Besides studying the influence of the absolute fiber temperature of a fixed fiber section, the impact of the length and position of the temperature-controlled fiber sections is investigated in experiments and simulations. Recompression-induced generation of additional dispersive waves is realized via soliton tunneling through normal dispersive regions of varying length. In summary, this work demonstrates how different flat group velocity dispersion profiles with two ZDWs can be obtained in higher-order modes by controlling the temperature of liquid-core step-index fibers. The thereby strongly varied soliton dynamics result in significant modifications of the generated supercontinua.