Measurements of transverse energy flow are presented for neutral current deep-inelastic scattering events produced in positron-proton collisions at HERA. The kinematic range covers squared momentum transfers Q2 from 3.2 to 2 200 GeV 2, the Bjorken scaling variable x from 8ot10-5 to 0.11 and the hadronic mass W from 66 to 233 GeV. The transverse energy flow is measured in the hadronic centre of mass frame and is studied as a function of Q2, x, W and pseudorapidity. A comparison is made with QCD-based models. The behaviour of the mean transverse energy in the central pseudorapidity region and an interval corresponding to the photon fragmentation region are analysed as a function of Q2 and W.