Thermoelectric energy harvesting (TEH) systems provide a sustainable means of powering emerging applications such as Internet of Things (IoT) devices, wearable electronics, and autonomous sensors. However, the inherently low and variable output voltage of thermoelectric generators (TEGs), compounded by dynamic thermal gradient fluctuations, poses significant challenges for stable and efficient power conditioning. This paper presents a Multi-Index Nonlinear Robust Adaptive Control (MINRAC) scheme for multilevel DC-DC converters in TEH systems. The proposed controller simultaneously addresses multiple performance objectives, including output voltage regulation, conversion efficiency, and component stress minimization. By integrating adaptive parameter estimation, nonlinear compensation, and robust disturbance rejection, MINRAC ensures asymptotic stability and accurate voltage tracking even under severe uncertainties and disturbances. The effectiveness of the approach is validated through MATLAB/Simulink and Python-based simulations, demonstrating superior performance compared to proportional-integral (PI) and sliding mode control (SMC) strategies. Results highlight MINRAC's ability to deliver improved transient response, reduced steady-state error, and enhanced robustness to thermal variations, thereby enabling reliable and high-efficiency energy harvesting for next-generation batteryless electronic systems.