The postmortem interval (PMI), i.e. the time since death, plays a key role in forensic investigations, as it aids in the reconstruction of the timeline of events. Currently, the standard method for PMI estimation empirically correlates rectal temperatures and PMIs, frequently necessitating subjective correction factors. To address this shortcoming, numerical thermodynamic algorithms have recently been developed, providing rigorous methods to simulate postmortem body temperatures. Comparing these with measured body temperatures then allows non-subjective PMI determination. This approach, however, hinges on knowledge of two thermodynamic input parameters, which are often irretrievable in forensic practice: the ambient temperature prior to discovery of the body and the body temperature at the time of death (perimortem). Here, we overcome this critical limitation by combining numerical thermodynamic modelling with surrogate model-based parameter optimization. This hybrid computational framework predicts the two unknown parameters directly from the measured postmortem body temperatures. Moreover, by substantially reducing computation times (compared with conventional optimization algorithms), this powerful approach is uniquely suited for use directly at the crime scene. Crucially, we validated this method on deceased human bodies and achieved the lowest PMI estimation errors to date (0.18 h ± 0.77 h). Together, these aspects fundamentally expand the applicability of numerical thermodynamic PMI estimation.