Abstract: The numerical modeling of the magnetic field evolution in astrophysical scenarios is essential for the understanding of systems such as magnetars and highly magnetic pulsars. The governing equation of the magnetic field evolution in the crust of a neutron star is the Hall induction equation. In this equation, the relative contribution of the Hall term and Ohmic dissipation varies depending on the local conditions of temperature and magnetic field strength. Besides, the strong magnetic field of neutron stars is coupled to the observed temperature, spectral properties, as well as timing properties. In this work, we present the results of 2D magneto-thermal simulations varying different parameters: initial magnetic field, equation of state and mass. A comparison of models to the data obtained from X-ray observations is discussed, for a better understanding of different classes of neutron stars.