Introduction: This exploratory study investigated whether performance in a behavioural inhibition task followed the shape proposed by the Maximum Adaptability Model during progressive exertional heat stress—that is, an initial improvement in cognitive performance is followed by a plateau, and subsequent decline once body temperature continues to rise unabated. Methods: Seventeen adult males walked on a treadmill at 4 km h−1 (1% grade) for up to 120 min, in three protective clothing ensembles, across three simulated environments. The simulated environments were equivalent to wet bulb globe temperatures 21, 30 and 37 °C. Cognitive function was assessed using a modified colour-word Stroop Task, with performance expressed as inverse efficiency scores in the simple (congruent) and more complex (incongruent) task conditions. The Stroop Task was completed before a trial, at termination, and every 30 min during walking, and core body temperature was continuously measured. Data were modelled using Bayesian penalised regression, with core body temperature included as a non-linear term (i.e., second degree polynomial). Results: We did not find any evidence that core body temperature had an effect on congruent or incongruent inverse efficiency scores, and no evidence that the relationship between these variables followed the shaped described by the Maximum Adaptability Model. There was, however, evidence that higher pre-exercise serum osmolality values were associated with slower congruent (β = 9.19) and incongruent (β = 8.67) inverse efficiency scores. The posterior probability that these effects were greater than zero was 0.971 and 0.952, respectively. Conclusions: In young, fit men, performance in the behavioural inhibition task was unaffected by increases in body temperature up to 39 °C and did not follow the shape proposed by the Maximum Adaptability Model. A secondary finding of the study was that pre-exercise hydration status affected performance in the inhibition task. Future studies are needed to confirm this result.