In this article, a comprehensive geometrical–mechanical–thermal predictive model is developed for thermal contact conductance between two flat metallic rough surfaces. The rough surface was characterized by Weierstrass–Mandelbrot fractal function. The micro-morphology was measured by laser microscope to identify the fractal parameters that were then applied to mechanical and thermal modeling. A new contact mechanics model was then proposed to calculate the contact parameters, and different contact scales between asperities and three modes of deformation, elastic, elastic–plastic and fully plastic, were taken into account. The normal contact pressure, which should be equal to the exterior load, was formulated as a function of the fractal parameters, the maximum contact area and the material physical properties of the given surface. Based on the contact mechanics model, first a single pair of contacting asperities was proposed and then multi-contacting asperities were combined to get total thermal contact conductance. The influences of contact load, surface roughness, asperity top radius and contact area as well as the temperature on the thermal contact conductance were investigated by using the proposed model. The investigation results showed that thermal contact conductance increases with the contact load and contact area. The larger the surface roughness, the smaller is the thermal contact conductance. Finally, the experiments were conducted to validate the effectiveness of the thermal contact conductance modeling. This geometrical–mechanical–thermal predictive model was compared with the two existing predictive models and a series of experimental data. The results showed good agreement, demonstrating the validity of the model and providing certainty for further study on the heat transfer between contact surfaces.