To understand the exhumation history of the Alpine foreland, it is important to accurately reconstruct its time-temperature evolution. This is often done employing thermokinematic models. One problem of many current approaches is that they are limited to 2-D and do not consider structural or kinematic uncertainties. In this work, we combine 3-D kinematic forward modeling with a systematic random sampling approach to automatically generate an ensemble of kinematic models in the range of assigned geometric uncertainties. Using Markov chain Monte Carlo, each randomly generated model will be assessed in regards to how well they fit the available thermochronology data. This is done to obtain an updated set of modeling parameters with reduced uncertainty. The resulting, more robust model can then be used to re-interpret the thermochronological data and find alternative drivers of cooling for certain samples.We apply this approach to a simple synthetic model to test the methodology, and then to the Eastern Alps triangle zone in the Bavarian Subalpine Molasse. Results show that it is possible to translate low-temperature thermochronology data into a likelihood function to obtain a 3-D kinematic model with updated, more probable parameters. The thermochronological data by itself, however, may not be informative enough to reduce the parameter uncertainty. The method is useful, however, to study alternative mechanisms of exhumation for the thermochronological samples that are not respected by the modeling, even when uncertainty is considered.