  With the assumption of local Tsallis equilibrium, the newly defined
gravitational temperature is calculated in the solar interior, whose
distribution curve can be divided into three parts, the solar core region,
radiation region and convection region, in excellent agreement with the solar
hierarchical structure. By generalizing the Fourier law, one new mechanism of
heat conduction, based on the gradient of the gravitational temperature, is
introduced into the astrophysical system. This mechanism is related to the
self-gravity of such self-gravitating system whose characteristic scale is
large enough. It perhaps plays an important role in the astrophysical system
which, in the solar interior, leads to the heat accumulation at the bottom of
the convection layer and then motivates the convection motion.
