In this paper, a two dimensional mathematical model of steady temperature fluctuation with convention is studied. A formal Fourier series solution of the model is proved convergent, and the solution of the mathematical model is unique and steady. The melt temperature shows both periodical pattern along the horizontal direction relative to crystal growth, and oscillatory and exponentially decay along the crystal growth. It theoretically confirms that the mechanism of melt nucleation that the horizontal melt convection condition leads to the local supercool temperature and accelerates temperature fluctuation and results in the large number of nuclei.