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This paper describes the numerical investigation of two thermal related problems in heat assisted magnetic recording: 1) the dependence of the recorded mark width on the laser power and 2) the temperature distribution of the lubricant layer and its variation with time and the change with and without the heat sink layer. It is found that the mark width increases with the increase of laser power, but the increase is not linear due to the Gaussian distribution of the laser intensity. It is also found that in certain power range, a smaller laser spot will generate a wider mark width at the same laser power. For lubricant cooling process, the temperature in lubricant layer decreases quickly after the laser is removed. Within 0.5 ns, the maximum temperature in lubricant layer drops 35.6degC when there is no heat sink layer applied under the recording media layer. With heat sink layer applied under the media layer, the temperature drop is even faster and decreases by 57.0degC in 0.5 ns. Hence, the heat sink layer is useful to quickly cool the lubricant layer to a thermally stable range.