This thesis presents the results from the Chandra Deep Group Survey, a survey dedicated to find high redshift groups of galaxies in deepest observations available in the Chandra archive. The catalogue compiled from this survey contains 26 groups and 36 clusters with available redshifts, with largest redshift being 1.3. This sample has been used to investigate the evolution of the thermal state of the gas at the centre of groups and compare this evolution to that of clusters. Different parameters have been used to quantify the strength of cool cores and it has been showed that groups and clusters have similar evolution of their cool core properties. Both classes of systems have a wide spread in the cool core strength at low redshifts, which then narrows at high redshifts showing a lack of strong cool core systems.