This paper presents high power, thermal analyses, and implementation of a stepped impedance high-power low-pass filter (LPF). A comprehensive model and analysis have been developed for the design and simulation of the LPF. In this analysis, power handling capacity and breakdown-voltage are discussed, and the effects of critical points are considered. The attenuation due to conductor and dielectric losses is also studied. The novelty of our approach lies in employing theoretical analysis to estimate the power-dissipation of the filter based on the proposed equivalent circuit. An accurate method is also introduced to calculate attenuation in the filter's elements. Thermal analysis to obtain accurate temperature profiles is done for the first time based on the electro-thermal simulation. Consequently, an effective cooling method is used to spread heat across the entire filter. Finally, the filter was implemented and tested to operate at L-band with handling 8 kW peak and 800 W average power. The insertion-loss is less than 0.27 dB, the stop-band attenuation is more than 60 dB, and the return-loss is better than 15.7 dB. The filter is capable of tolerating produced heat without any destructive effects at a maximum temperature of about 200 C above ambient. The theoretical analysis and experimental results show that the LPF is suitable for high-power microwave applications.