Therapeutic hypothermia improves outcomes following neonatal hypoxic-ischaemic encephalopathy, reducing cases of death and severe disability such as cerebral palsy compared with normothermia management. However, when cooled children reach early school-age, they have cognitive and motor impairments which are associated with underlying alterations to brain structure and white matter connectivity. It is unknown whether these differences in structural connectivity are associated with differences in functional connectivity between cooled children and healthy controls. Resting-state functional MRI has been used to characterize static and dynamic functional connectivity in children, both with typical development and those with neurodevelopmental disorders. Previous studies of resting-state brain networks in children with hypoxic-ischaemic encephalopathy have focussed on the neonatal period. In this study, we used resting-state fMRI to investigate static and dynamic functional connectivity in children aged 6-8 years who were cooled for neonatal hypoxic-ischaemic without cerebral palsy [n = 22, median age (interquartile range) 7.08 (6.85-7.52) years] and healthy controls matched for age, sex and socioeconomic status [n = 20, median age (interquartile range) 6.75 (6.48-7.25) years]. Using group independent component analysis, we identified 31 intrinsic functional connectivity networks consistent with those previously reported in children and adults. We found no case-control differences in the spatial maps of these intrinsic connectivity networks. We constructed subject-specific static functional connectivity networks by measuring pairwise Pearson correlations between component time courses and found no case-control differences in functional connectivity after false discovery rate correction. To study the time-varying organization of resting-state networks, we used sliding window correlations and deep clustering to investigate dynamic functional connectivity characteristics. We found k = 4 repetitively occurring functional connectivity states, which exhibited no case-control differences in dwell time, fractional occupancy or state functional connectivity matrices. In this small cohort, the spatiotemporal characteristics of resting-state brain networks in cooled children without severe disability were too subtle to be differentiated from healthy controls at early school-age, despite underlying differences in brain structure and white matter connectivity, possibly reflecting a level of recovery of healthy resting-state brain function. To our knowledge, this is the first study to investigate resting-state functional connectivity in children with hypoxic-ischaemic encephalopathy beyond the neonatal period and the first to investigate dynamic functional connectivity in any children with hypoxic-ischaemic encephalopathy.