Sensing environmental temperatures is essential for the survival of ectothermic organisms. In Drosophila, two of the most used methodologies to study temperature preferences (TP) and the genes involved in thermosensation are two-choice assays and temperature gradients. Whereas two-choice assays reveal a relative TP, temperature gradients can identify the absolute Tp. One drawback of gradients is that small ectothermic animals are susceptible to cold-trapping: a physiological inability to move at the cold area of the gradient. Often cold-trapping cannot be avoided, biasing the resulting TP to lower temperatures. Two mathematical models were previously developed to correct for cold-trapping. These models, however, focus on group behaviour which can lead to overestimation of cold-trapping due to group aggregation. Here we present a mathematical model that simulates the behaviour of individual Drosophila in temperature gradients. The model takes the spatial dimension and temperature difference of the gradient into account, as well as the rearing temperature of the flies. Furthermore, it allows the quantification of cold-trapping and reveals unbiased TP. Additionally, our model reveals that flies have a range of tolerable temperatures, and this measure is more informative about the behaviour than commonly used TP. Online simulation is hosted at http://igloo.uni-goettingen.de . The code can be accessed at https://github.com/zerotonin/igloo .