In this paper, a double-mode self-calibration tension system is proposed, which adopts the conversion of hydraulic meter tension and the monitoring of standard force sensors. According to the material characteristics of the jack and the viscosity and temperature characteristics of the hydraulic oil, the differential model of heat conduction in the hydraulic cylinder and the mathematical model of oil film friction heat generation are established, and the internal thermodynamic characteristics of the jack are theoretically analyzed, which provides theoretical support for the temperature compensation of the hydraulic oil pressure gauge of the jack. A simulation analysis was conducted on the thermodynamic characteristics of the hydraulic jack, and the distribution patterns of the temperature field, thermal stress field, and thermal strain field inside the hydraulic cylinder during normal operation were determined by measuring the temperature changes in five different parts of the jack at different times (t = 200 s, 2600 s, 5000 s, 7400 s, and 10,000 s). For the issue of heat generation due to oil film friction in the hydraulic jack, a simulation calculation model is developed by integrating Computational Fluid Dynamics (CFD) techniques with dynamic grid and slip grid methods. By simulating and analyzing frictional heating under conditions where the inlet pressures are 0.1 MPa, 0.3 MPa, 0.5 MPa, 0.7 MPa, and 0.9 MPa, respectively, we can obtain the temperature distribution on the jack, determine the frictional resistance, and subsequently conduct a theoretical analysis of the simulation results. Using the high-precision standard force sensor after data processing and the hydraulic oil gauge after temperature compensation, the online self-calibration of the tensioning system is carried out, and the regression equation of the tensioning system under different oil temperatures is obtained. The double-mode self-calibration tensioning system with temperature compensation is used to verify the compensation accuracy of the proposed double-mode self-calibration tensioning system.