Deterministic forward models are commonly used to quantify the processes accompanying basin evolution. Here, we describe a workflow for the rapid calibration of palaeo heat-flow behaviour. The method determines the heat-flow history which best matches the observed data, such as vitrinite reflectance, which is used to indicate the thermal maturity of a sedimentary rock. A limiting factor in determining the heat-flow history is the ability of the algorithm used in the software for the maturity calculation to resolve information inherent in the measured data. Thermal maturation is controlled by the temperature gradient in the basin over time and is therefore greatly affected by maximum burial depth. Calibration, i.e. finding the thermal history model which best fits the observed data (e.g. vitrinite reflectance), can be a time-consuming exercise. To shorten this process, a simple pseudo-inverse model is used to convert the complex thermal behaviour obtained from a basin simulator into more simple behaviour, using a relatively simple equation. By comparing the calculated "simple" maturation trend with the observed data points using the suggested workflow, it becomes relatively straightforward to evaluate the range within which a best-fit model will be found. Reverse mapping from the simple model to the complex behaviour results in precise values for the heat-flow which can then be applied to the basin model. The goodness-of-fit between the modelled and observed data can be represented by the Mean Squared Residual (MSR) during the calibration process. This parameter shows the mean squared difference between all measured data and the respective predicted maturities. A minimum MSR value indicates the "best fit". Case studies are presented of two wells in the Horn Graben, Danish North Sea. In both wells calibrating the basin model using a constant heat-flow over time is not justified, and a more complex thermal history must be considered. The pseudo-inverse method was therefore applied iteratively to investigate more complex heat-flow histories. Neither in the observed maturity data nor in the recorded stratigraphy was there evidence for erosion which would have influenced the present-day thermal maturity pattern, and heat-flow and time were therefore the only variables investigated. The aim was to determine the simplest "best-fit" heat-flow history which could be resolved at the maximum resolution given by the measured maturity data. The conclusion was that basin models in which the predicted maturity of sedimentary rocks is calibrated solely against observed vitrinite reflectance data cannot provide information on the timing of anomalies in the heat-flow history. The pseudo inverse method, however, allowed the simplest heat-flow history that best fits the observed data to be found.