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Precise temperature measurements on systems of few ultracold atoms is of paramount importance in quantum technologies, but can be very resource-intensive. Here, we put forward an adaptive Bayesian framework that substantially boosts the performance of cold atom temperature estimation. Specifically, we process data from real and simulated release--recapture thermometry experiments on few potassium atoms cooled down to the microkelvin range in an optical tweezer. From simulations, we demonstrate that adaptively choosing the release--recapture times to maximise information gain does substantially reduce the number of measurements needed for the estimate to converge to a final reading. Unlike conventional methods, our proposal systematically avoids capturing and processing uninformative data. We also find that a simpler non-adaptive method exploiting all the a priori information can yield competitive results, and we put it to the test on real experimental data. Furthermore, we are able to produce much more reliable estimates, especially when the measured data are scarce and noisy, and they converge faster to the real temperature in the asymptotic limit. Importantly, the underlying Bayesian framework is not platform-specific and can be adapted to enhance precision in other setups, thus opening new avenues in quantum thermometry.