Denoising is a key problem in phase extraction for electronic speckle pattern interferometry (ESPI) fringe. The heat conduction equation (HCE) is applied to denoise for ESPI fringe patterns and its filtering performance is analyzed qualitatively and quantitatively. Based on the HCE filtered result, MBO algorithm and HCE are applied further to binarization and phase map smoothing respectively. And the phase map of the fringe is extracted successfully from a single fringe pattern. The research shows that HCE can efficiently reduce the noise of speckle fringe pattern, improve the edge of binary fringe pattern, and perform phase recovery rather accurately.