Thermo-hydrodynamic (THD) lubrication is a key mechanism in injection pumps, where frictional heating and heat transfer strongly influence lubrication performance. Accurate numerical modeling remains challenging due to the nonlinear coupling of temperature- and pressure-dependent fluid properties and the high computational cost of iterative solvers. The rising relevance of bio-hybrid fuels, however, demands the investigation of a great number of fuel mixtures and conditions, which is currently infeasible with traditional solvers. Physics-informed neural networks (PINNs) have recently been applied to lubrication problems; existing approaches are typically restricted to stationary cases or rely on data to improve training. This work presents a novel, purely physics-based PINN framework for solving coupled, transient THD lubrication problems in injection pumps. By embedding the Reynolds equation, energy conservation laws, and temperature- and pressure-dependent fluid models directly into the loss function, the proposed approach eliminates the need for any simulation or experimental data. The PINN is trained solely on physical laws and validated against an iterative solver for 16 transient test cases across two fuels and eight operating scenarios. The good agreement of PINN and iterative solver demonstrates the strong potential of PINNs as efficient, scalable surrogate models for transient THD lubrication and iterative design applications.