  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.
