Thermal contact resistance (TCR) plays a pivotal role in heat transfer across diverse engineering applications. The present work systematically investigates TCR for two representative contact configurations, namely flat and hinge-type curved surfaces, under varied conditions of temperature, pressure, and surface roughness. A high-precision steady-state heat flux experimental system was designed, integrating heating, cooling, and pressure-loading subsystems to ensure controlled operation conditions. The experimental results revealed that TCR decreases with rising contact temperature and pressure, while it increases significantly with surface roughness. And the surface roughness exerts the most dominant influence. The effect of pressure on TCR is relatively minor at smaller surface roughness, whereas the pressure dependence becomes more significant at larger roughness. Empirical correlations for TCR as functions of contact pressure, roughness, and temperature were formulated for both flat and curved surface contacts based on the experimental data. The maximum fitting errors of the correlations are 6% for flat surface contact and 9.2% for curved surface contact, which demonstrates the reliability of the fitting results. These relationships enable the theoretical calculation of TCR for both flat and curved surface contacts under varying operating conditions.