Wet clutches are widely employed in both fuel and hybrid electric vehicles. Accurate control of wet clutch pressure via a proportional solenoid valve is essential for regulating the torque transmitted during launch, gear shifts, and mode transitions, ensuring fuel efficiency, safety, and vehicle comfort. However, maintaining precise clutch pressure control remains challenging due to the complex nonlinearity of the clutch electro-hydraulic actuator (EHA) and oil temperature variations. Modeling the pressure of the EHA to accurately reflect its temperature-dependent nonlinearity is crucial for achieving precise control. In this study, we analyze the pressure responses of the EHA under rectangular and triangular pulse signals of varying rates and amplitudes, considering the input signal characteristics during the oil-filling and pressure regulation stages across a specific oil temperature range. We propose phenomenological model that describe the nonlinear characteristics, such as pressure hysteresis and saturation of the EHA, over this temperature range. Experimental data are used to identify key parameters of the phenomenological model. Finally, the validity of the proposed model is verified and analyzed under different oil temperature conditions.