The heat output and thermal regime of fast and intermediate spreading centers are strongly controlled by boundary layer processes between the hydrothermal system and the underlying crustal magma chamber (AMC), which remain to be fully understood. Here, we model the interactions between a shallow two-dimensional cellular hydrothermal system at temperatures <700°C, and a deeper AMC at temperatures up to 1200°C. We show that hydrothermal cooling can freeze the AMC in years to decades, unless melt injections occur on commensurate timescales. Moreover, the differential cooling between upflow and downflow zones can segment the AMC into mush and melt regions that alternate on sub-kilometric length scales. These predictions are consistent with along-axis variations in AMC roof depth observed in ophiolites and oceanic settings. In this respect, fine-scale geophysical investigations of the structure of AMCs may help constrain hydrothermal recharge locations associated with active hydrothermal sites.