Earth's magnetic field is recorded as oceanic crust cools, generating lineated magnetic anomalies that provide the pattern of polarity reversals for the past 160 million years1. In the lower (gabbroic) crust, polarity interval boundaries are proxies for isotherms that constrain cooling and hence crustal accretion. Seismic observations2-4, geospeedometry5-7 and thermal modelling8-10 of fast-spread crust yield conflicting interpretations of where and how heat is lost near the ridge, a sensitive indicator of processes of melt transport and crystallization within the crust. Here we show that the magnetic structure of magmatically robust fast-spread crust requires that crustal temperatures near the dike-gabbro transition remain at approximately 500degreesCelsius for 0.1millionyears. Near-bottom magnetization solutions over two areas, separated by approximately 8kilometres, highlight subhorizontal polarity boundaries within 200metres of the dike-gabbro transition that extend 7-8kilometres off-axis. Oriented samples with multiple polarity components provide direct confirmation of a corresponding horizontal polarity boundary across an area approximately onekilometre wide, and indicate slow cooling over three polarity intervals. Our results are incompatible with deep hydrothermal cooling within a few kilometres of the axis2,7 and instead suggest a broad, hot axial zone that extends roughly 8 kilometres off-axis in magmatically robust fast-spread ocean crust.