Magnetic fluctuations through the molecular cloud cores can produce ambipolar diffusion (AD) heating, which consequently can produce temperature gradients through the core. The aim of this paper is to investigate the effects of these produced temperature gradients on the radius and mass of the non-isothermal modified Bonnor-Ebert spheres (MBES). Here, we use the parameter $\kappa$ to represent the magnetic fluctuations through the molecular cloud cores. This parameter introduces the change of magnetic filed strength in the length-scale. The results show that increasing of $\kappa$ leads to an increase of the radius and mass of MBES. The most important result is existence of the gravitationally stable high-mass prestellar cores at the low-density molecular medium with great magnetic fluctuations.
