Thermotolerance is a major determinant of ectotherm geographic distribution, but the physiological mechanisms underlying cold tolerance remain poorly understood. A critical uncertainty is whether basal thermotolerance constrains plastic thermotolerance, such that animals with greater basal tolerance have a lower capacity for acclimation. To address this question, a trade-off between basal and plastic thermal tolerance has been tested at several levels in insects (e.g. lineage, species, and population), often with conflicting results. If basal tolerance constrains plasticity through shared mechanisms of tolerance, however, it should be evident at the level of the individual over multiple trials, provided the trait measured is repeatable. Here, we used chill-coma onset temperature (CCO; a non-lethal thermal limit) to quantify cold tolerance of individual Drosophila melanogaster across two trials (pre- and post-acclimation). Overall, cold acclimation significantly improved cold tolerance, as expected. However, measurements of CCO in control flies (that were not cold-acclimated) were not repeatable and yet, surprisingly, degree of plasticity was still related to basal tolerance. We argue that this relationship is an artefact of the most common method for testing for such trade-offs and does not reflect a true trade-off or physiological constraint. More broadly, our data suggests that cold tolerance traits (or at least CCO) lack the intraindividual repeatability necessary to test for thermal plasticity constraints at this level. Altogether, our work supports previously voiced concerns about common practices for testing tolerance-plasticity trade-offs, and we propose a new approach for addressing these questions.