Cryogenic rocket engines offer the highest specific impulse among liquid rocket engines, making them a crucial component of space missions. Cryogenic engines are mostly used in the upper stage of the rocket. Maintaining precise control over the Mixture Ratio (MR) in liquid rocket engine is vital, and it is achieved by bypassing a portion of the liquid oxygen (LOX) from the pump's delivery side to its suction side. However, this MRC bypass flow mixing results in non-uniform temperature at the pump inlet, which may get further aggravated in the pump leading to non-uniform temperature at the thrust chamber injector inlet. This non-uniform injection temperature may cause combustion related problems. This paper presents a comprehensive computational fluid dynamics (CFD) study conducted to investigate the flow characteristics in two distinct cases: Constant pump inlet temperature flow (Case 1) and Maximum MRC bypass flow condition (Case 2). In Case 2, the pump inlet temperature variation of 3.2 K decreased to 2.1 K at the pump delivery and further mixed in the downstream elbow, resulting in a temperature variation of 0.4 K only. On the other hand, in Case 1, the constant pump inlet temperature flow exhibited a non-uniformity of temperature of approximately 1.9 K at pump outlet, which diminished significantly to an order of 0.1 K in the downstream line. The pump performance (headrise and efficiency) obtained from CFD closely matches with performance of pump during the hot test.