Thermal contact resistance (TCR) between metallic rough surfaces plays a significant role in thermal management of electronic devices. In this work, the roughness is depicted by the fractal geometry theory and constructed by the Weierstrass-Mandelbrot (W-M) function. The influence of model parameters on rough surface is studied. Then the surface deformation analysis is conducted to calculate the actual area of contact. The influence of pressure on actual contact area is revealed. After that, the mesh is generated and the steady heat conduction equation is discretized using the finite difference (FD) method. The thermal conductivity at the interface node is equal to the harmonic mean thermal conductivity of two adjacent nodes. The discretized heat conduction equation is solved by iterative method. The convergence criterion is that the residual error of temperature is less than 10^-6. We find that the main temperature change occurs at the contact interface. Even under high pressure, the temperature jump at the interface is still large due to the low actual contact area. The TCR is also affected by the number and distribution of actual contact spots. The interface temperature jump and TCR can be effectively reduced by increasing the thermal conductivity of gap fluid. Thus the key to reduce TCR is to use thermal interface materials with high thermal conductivity in practical engineering applications.