In recent years the concept of Digital Twins (DTs) has gained significant attention, in particular in the manufacturing industry. In proper DTs there is a bidirectional connection to/from their Physical Twins such that it is possible to leave humans out of the loop. However, the underlying ideas of DTs have been inspired from a number of different scientific communities, in particular in relation to autonomy including the 'Monitor-Analyze-Plan-Execute over a shared Knowledge' (MAPE-K). In this paper, we bridge the two concepts by demonstrating an implementation of a MAPE-K loop for an incubator case study within the context of its DT. We also discuss some of the limitations of the MAPE-K concept when applied to Cyber-Physical Systems (CPS).