Trait Intellect, one of the two ‘aspects’ of the broader Openness/Intellect ‘domain’, predicts performance on a range of cognitive tasks including tests of intelligence and working memory. This has been explained in terms of the tendency for high‐Intellect individuals to explore, or engage more effortfully with, abstract information. This theoretical perspective can be framed in the language of Resource Allocation Theory, in terms of high‐Intellect individuals allocating more of their available cognitive resources to abstract cognitive tasks. In two experiments (total N = 160), we examined the relation between Intellect and cognitive engagement during a primary word‐search task under conditions of both high and low secondary cognitive load. Both experiments revealed that high‐Intellect individuals were more vulnerable to the impact of the secondary cognitive load on primary task performance. This suggests that, under low secondary load, such individuals were indeed allocating more of their available cognitive resources to the primary task. These results held after controlling for trait Openness, trait Industriousness (an aspect of Conscientiousness) and a measure of working memory capacity (N‐back task). Our findings provide novel support for the cognitive mechanisms proposed to underlie trait Intellect.