Background: Although supplemental oxygen can be lifesaving, liberal oxygen administration causing hyperoxaemia may be harmful. The targets for oxygenation in patients with acute hypoxaemic respiratory failure acutely admitted to the intensive care unit (ICU) are strongly debated, and consensus on which targets to recommend has not been reached. The Handling Oxygenation Targets in the ICU (HOT-ICU) trial is a multicentre, randomised, parallel-group trial of a lower oxygenation target (arterial partial pressure of oxygen [PaO₂] = 8 kPa) versus a higher oxygenation target (PaO₂ = 12 kPa) in adult ICU patients with acute hypoxaemic respiratory failure. In this study, we aim to evaluate the effects of these targets on long-term cognitive and pulmonary function in Danish patients, enrolled in the HOT-ICU trial and surviving to 1-year follow-up. We hypothesise that a lower oxygenation target throughout the ICU stay may result in cognitive impairment, whereas a higher oxygenation target may result in impaired pulmonary function. Methods: All patients enrolled in the HOT-ICU trial at Danish sites and surviving to 1 year after randomisation are eligible to participate. The last patient is expected to be included by November 2021. A Repeatable Battery for the Assessment of Neuropsychological Status and a body plethysmography, including diffusion capacity for carbon monoxide, both pre-planned secondary long-term outcomes of the HOT-ICU trial, will be obtained. Conclusion: This study will provide important information on the long-term effects of a lower versus a higher oxygenation target on cognitive and pulmonary function in adult ICU patients with acute hypoxaemic respiratory failure.