Motivated by design challenges related to aerospace propulsive jets, an experimental investigation has been conducted of the high Mach number jet plume flow field from a round convergent nozzle at under-expanded shock-containing conditions. Hot jets up to a total temperature ratio of 3 were considered. Laser doppler anemometry (LDA) measurements in the jet near field (first 15 nozzle exit diameters) captured the turbulent mixing process in detail, enabling the separate effects of compressibility and static temperature ratio (t) on the development of the velocity and turbulence profiles to be identified. Compressibility dominated in the initial shear layer region, whereas temperature effects controlled the downstream jet merging zone. Analysis of shear layer development demonstrated that, at all temperature ratios, a similar, but significantly stronger, damping effect was observed as in planar shear layers (correlated well by convective Mach number Mc). Consideration of the interaction of compressibility and temperature ratio – which reduce/enhance turbulent mixing respectively – provided for the first time a rational explanation of the observation that increasing jet temperature influenced flow development only up to a static temperature ratio t ~ 1.5, after which further increase has little effect. Measurements of the potential core length (Lp) were analysed to produce an empirical correlation that also illustrated the diminishing effects of heat addition at all jet Mach numbers. The data provide the improved understanding and empirical design techniques essential for developing technologies for jet noise and infra red (IR) signature reduction and represent an important validation test case for computational fluid dynamics (CFD) modelling.