Individuals tend to avoid cognitive demand, yet, individual differences appear to exist. Recent evidence from two studies suggests that individuals high in the personality traits Self-Control and Need for Cognition that are related to the broader construct Cognitive Effort Investment are less prone to avoid cognitive demand and show less effort discounting. These findings suggest that cost-benefit models of decision-making that integrate the costs due to effort should consider individual differences in the willingness to exert mental effort. However, to date, there are almost no replication attempts of the above findings. For the present conceptual replication, we concentrated on the avoidance of cognitive demand and used a longitudinal design and latent state-trait modeling. This approach enabled us to separate the trait-specific variance in our measures of Cognitive Effort Investment and Demand Avoidance that is due to stable, individual differences from the variance that is due to the measurement occasion, the methods used, and measurement error. Doing so allowed us to test the assumption that self-reported Cognitive Effort Investment is related to behavioral Demand Avoidance more directly by relating their trait-like features to each other. In a sample of N = 217 participants, we observed both self-reported Cognitive Effort Investment and behavioral Demand Avoidance to exhibit considerable portions of trait variance. However, these trait variances were not significantly related to each other. Thus, our results call into question previous findings of a relationship between self-reported effort investment and demand avoidance. We suggest that novel paradigms are needed to emulate real-world effortful situations and enable better mapping between self-reported measures and behavioral markers of the willingness to exert cognitive effort.