Measurements of transverse energy flow for neutral current deep- inelastic scattering events produced in positron-proton collisions at HERA. The kinematic range covers squared momentum transfers $Q^2$ from 3.2 to 2200 GeV$^2$; the Bjorken scaling variable $x$ from $8 \times 10^{-5}$ 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 $Q^2$, $x$, $W$ and pseudorapidity. 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 $Q^2$ and $W$. This analysis is useful for exploring the effect of photon PDFs and for tuning models of parton evolution and treatment of fragmentation and the proton remnant in DIS.