We present a perturbative calculation of the energy profile width of rigid strings up to two loops in D dimensions. The perturbative expansion of the extrinsic curvature term, signifying the rigidity/smoothness of the string in Polyakov-Kleinert action, is taken around the free Nambu-Goto string. The mean-square width of the string field is derived for open strings with the Dirichlet boundary condition. We compare the broadening of the smooth Polyakov-Kleinert string to the lattice Monte Carlo data of the QCD flux tube just before the deconfinement point and find a good match at the intermediate and large color source separation.