Brownian motion, often known as BM, is an inherent characteristic of minute particles suspended in a fluid. It plays an important role in several physical and chemical processes. Thermophoresis refers to the process where particles in a fluid are carried along with a gradient in temperature (Temp). This feature has significant importance in several applications, including microfluidics, thermal control, and energy conversion. Through the examination of the thermophoresis phenomenon in water/graphene nanofluid (NF), researchers might get valuable knowledge on the potential uses of these materials. The current study examined the effect of various sizes of graphene nanoparticles (NPs) (5, 6, 9, and 10 Å) on the thermal behavior (TB), BM, and thermophoresis of water/graphene NF using molecular dynamics (MD) simulation. This study reported the changes in heat flux (HF), thermal conductivity (TC), average Brownian displacement (BD), and thermophoresis. It is concluded that by increasing the size of graphene NPs from 5 to 10 Å, the average BD and thermophoresis increased from 3.06 Å and 23.88 Å to 4.16 Å and 31.46 Å, respectively. Due to their higher kinetic energy (KE) and momentum, larger graphene NPs experienced more BM, enabling them to withstand random thermal fluctuations more effectively than smaller particles. In addition, as the size of graphene NPs increased, the HF and TC values increased from 39.54 W/m2 and 0.36 W/(m.K) to 47.19 W/m2 and 0.51 W/(m.K) after 10 ns. Therefore, the size-dependent changes in BD and thermophoretic effects led to a simultaneous increase in HF and TC of the NF, which was attributed to the larger heat transfer (HT) surface area, improved HT properties, and synergistic effects of larger graphene NPs. The maximum (Max) temperature increases from 1415 K to 1504 K. These findings were useful in a variety of industries, particularly for improving TB in different NFs.