Brush seals are one of the most important dynamic seals used in oil and oil mist applications in industrial turbines and aviation. Flexible bristle structure is the main structural superiority of brush seals, which enables precise clearance control and high performance in compensating rotor transients. The viscous medium between the high-speed rotor surface and brush seal bristles generates a hydrodynamic lifting force that determines seal clearance and leakage rate in oil sealing applications. Shear heating at moderate and high rotor surface speeds results in an increase in temperature and stabilization of lifting force, which is known as high-speed lift stabilization. Strong temperature–viscosity dependency of lube oils possesses the need for a detailed analysis and understanding of the effect of shear heat on hydrodynamic lift of brush seals in oil applications. To provide a better understanding about the critical balance of hydrodynamic lift force with rotor speed, temperature, and pressure, this work presents an analytical study to investigate pressure profile and shear heat temperature rise in liquid sealing medium within the hydrodynamic lift clearance. A closed-form solution to pressure and temperature distribution in axial and radial directions has been obtained by solving continuity, Navier–Stokes, and thermal energy equations for brush seals. The thermal and pressure functions are evaluated for linear and nonlinear pressure drop approaches, and the results are compared with each other. Deviation in nonlinear and linear pressure, resulting temperature level differences, and effect of rotor speed are detailed within the content of this study. The provided closed-form functions for pressure and temperature profiles are useful for designers since these can be utilized for turbine operation conditions. Dynamic test rig design for high-speed leakage performance measurement of turbomachinery seals is detailed, where the test rig can also be adopted for stiffness, frictional heat, power loss, torque loss, and bucket tip stability testing in oil and air environment. The test setup can also be used for testing dynamic seals other than brush seals.