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Management of eruptions requires a knowledge of lava effusion rates, for which a safe thermal proxy is often used. However, this thermal proxy does not take into account the flow dynamics and is basically time‐independent. In order to establish a more robust framework that can link eruption rates and surface thermal signals of lavas measured remotely, we investigate the spreading of a hot, isoviscous, axisymmetric subaerial gravity current injected at constant rate from a point source onto a horizontal substrate. We performed laboratory experiments and found that the surface thermal structure became steady after an initial transient. We develop a theoretical model for a spreading fluid cooled by radiation and convection at its surface that also predicts a steady thermal regime. We show that, despite the model's simplicity relative to lava flows, it yields the correct order of magnitude for the effusion rate required to …