Hyperactive comets have attracted attention due to their high water production rate with an unclear mechanism, though some hypotheses are proposed to explain it. Based on the thermal theories of the comet nuclei, this paper studied a comet surface thermal model considering the sublimation of H₂O. In this paper, a method for solving the sublimation rate of water ice by infrared spectra is proposed. The method adopts the assumption of comet nucleus surface temperature roughness and uses the numerical solution of the Fredholm equation. We use the HRI-IR spectra (1.05-4.8 μm) data by EPOXI to analyze the pixel water sublimation rate of hyperactive comet 103P/Hartley2. The results show that the sublimation exists in most areas of the surface with or without surface roughness, and most of the water production rate (70% ~ 90%) may come from the comet nucleus. According to the sublimation law, it is estimated that the sublimation temperature of water ice on 103P is above 180K. If the dust-to-ice volume ratio is 3:1, the sublimation temperature is about 200-210K, which indicates that the water ice may sublimate underneath. This may explain why exposed water ice on the surface cannot be observed while the active fraction of this comet is up to 100%.