Aims: In previous studies the microbial kinetics of Escherichia coli K12 have been evaluated under static and dynamic conditions (Valdramidis et al. 2005, 2006). An acquired microbial thermotolerance following heating rates lower than 0.82 degrees C min(-1) for the studied micro-organism was observed. Quantification of this induced physiological phenomenon and incorporation, as a model building block, in a general microbial inactivation model is the main outcome of this work. Methods and Results: The microbial inactivation rate observed (k(obs)) under time-varying temperature conditions is studied and expressed as a function of the heating rate (dT/ dt). Hereto, a model building block related to the microbial physiology (k(phys)) under stress conditions is developed. Evaluation of the performance of the developed mathematical approach depicts that physiological adaptation is an essential issue to be considered when modelling microbial inactivation. Conclusions: Consideration, at a mathematical level, of microbial responses resulting in physiological adaptations contribute to the reliable quantification of the safety risks during food processing. Significance and Impact of the StudyBy taking into account the physiological adaptation, the microbiological evolution during heat processing can be accurately assessed, and overly conservative or fail dangerous food processing designs can be avoided.