The heat conduction equation is a parabolic differential equation and a type of second-order linear partial differential equation. By applying the finite difference scheme in the Crank-Nicolson method, the numerical solution of the heat conduction equation can be calculated. Obtaining numerical solutions with a high level of accuracy, Richardson extrapolation is required. The Crank-Nicolson approach scheme has a high level of accuracy, because the gap between numerical and analytical solutions is very small. Richardson extrapolation greatly influences the accuracy of numerical solutions, because the gap between analytical solution and numerical solutions with Richardson extrapolation is smaller than disparity in numerical solutions without Richardson extrapolation.