The ratio between the heat diffusion coefficients parallel and perpendicular to the magnetic field lines, χ || /χ ⊥ , influences the flattening of the temperature profile inside magnetic islands and the driving term of neoclassical tearing modes [R. Fitzpatrick. Phys. Plasmas 2, 825 (1995)]. The value of this anisotropy is, however, not easily accessible experimentally. This article presents a method to determine it from a systematic comparison of temperature measurements at magnetic islands to numerical heat diffusion simulations. The application of the method is demonstrated for a 2/1 magnetic island in the TEXTOR tokamak, where a heat diffusion anisotropy of 10 8 is observed. This is lower by a factor of 40 than predicted by Spitzer and Härm [L. Spitzer and R. Härm. Phys. Rev. 89, 997 (1953)] and a strong indication that the heat flux limit determines the flattening of the electron temperature across magnetic islands.