Operators in industrial manufacturing environments are under pressure to cope with increasing flexibility and complexity of work. The automation of manufacturing requires operators to adopt new techniques and shifts the focus from low-complexity repetitive tasks to dealing with the execution of high-complexity tasks in cooperation with machines. The emergence of wearable technologies makes it possible to equip operators with miniaturized sensors that may be used to determine the physical and mental stress experienced by operators. Process mining technologies are suited to analyze such sensor data in the context of the manufacturing process with the ultimate goal of improving the operator's well-being through re-organization of work and the work place. However, the storage and processing of such highly personalized data comes with many privacy challenges. Whereas there are many potential benefits, such as improve the work environment, there are also many justified reasons for operators to oppose the processing of their data. Apart from employee concerns, data protection regulations, such as EU GDPR (Europe's General Data Protection Regulation), imposes many compliance challenges for the design of a process mining systems dealing with personal data. We contribute an analysis of the privacy challenges of using process mining on data recorded from sensorized operators in human-centered industrial environments. Guided by privacy research and the regulation imposed by the GDPR, we describe guidelines for privacy in process mining systems.