The purpose of this study is to apply the technique of Cubic Spline, Cubic BSpline and Crank-Nicolson in one-dimensional heat equations with Dirichlet boundary conditions. Then, their accuracy of numerical methods are compared by computing their absolute error and relative error. Those results of the methods are calculated by using Matlab 2008 and Microsoft Visual Studio 2010 (C++). As the results, Crank- Nicolson is a good approximation solution since the result of relative error is quite close to the zero. Besides that, for interpolation method, cubic B-spline interpolation is found to give better results compare to the cubic spline interpolation since the relative error of cubic B-spline is better than cubic spline. Regarding to the findings, it can be seen clearly that the cubic spline, cubic B-spline and Crank-Nicolson are well approximated and give better results with smaller step size.