The current study highlights the transient numerical analysis of wickless heat pipes (thermosyphons) for the thermal management of electronic devices. The thermal performance of the thermosyphon is analyzed using both Copper Oxide (CuO) and Aluminium Oxide (Al2O3) Nano-fluids with their concentrations at 1% and 5%. Deionized water is employed as a reference case for comparison. The study is carried out for variable heat inputs to the thermosyphon ranging from 10-50 W for a time interval of 30 s. The idea is to analyze the effect of the evaporator heat input and the Nano-particles concentration on the temperature, heat transfer coefficient, thermal resistance, and effective thermal conductivity of the heat pipe. The results indicate that CuO Nano-particles at a 5% concentration lead to a maximum thermal resistance reduction of 4.31% at 50 W, while Alumina Nano-particles at the same concentration lead to a more substantial reduction of 6.66% at the same heat load. The evaporator temperature varies between 377.52 K to 374.99 K using deionized water, and 376.95 K to 374.29 K using CuO Nano-fluid (at 1% concentration). The heat pipe's evaporator attains its highest convective heat transfer coefficient (437.91 W/m2K) by using Alumina Nano-fluid with 1% Nano-particle concentration at 50 W. Moreover, the effective thermal conductivity of the heat pipe is enhanced by 5% and 7% for Copper Oxide and Aluminium Oxide Nano-fluids (with 5% concentration), respectively at 50 W.