Axial melt lenses sandwiched between the lower oceanic crust and the sheeted dike sequences at fast-spreading mid-ocean ridges are assumed to be the major magma source of oceanic crust accretion. According to the widely discussed ``gabbro glacier'' model, the formation of the lower oceanic crust requires efficient cooling of the axial melt lens, leading to partial crystallization and crystal-melt mush subsiding down to lower crust. These processes are believed to be controlled by periodical magma replenishment and hydrothermal circulation above the melt lens. Here we quantify the cooling rate above melt lens using chemical zoning of plagioclase from hornfelsic recrystallized sheeted dikes drilled from the East Pacific at the Integrated Ocean Drilling Program Hole 1256D. We estimate the cooling rate using a forward modelling approach based on CaAl-NaSi interdiffusion in plagioclase. The results show that cooling from the peak thermal overprint at 1000-1050°C to 600°C are yielded within about 10-30 years as a result of hydrothermal circulation above melt lens during magma starvation. The estimated rapid hydrothermal cooling explains how the effective heat extraction from melt lens is achieved at fast-spreading mid-ocean ridges.