  High-speed vehicles experience a highly challenging environment in which the
free-stream Mach number and surface temperature greatly influence aerodynamic
drag and heat transfer. The interplay of these two parameters strongly affects
the near-wall dynamics of high-speed turbulent boundary layers in a non-trivial
way, breaking similarity arguments on velocity and temperature fields,
typically derived for adiabatic cases. In this work, we present direct
numerical simulations of flat-plate zero-pressure-gradient turbulent boundary
layers spanning three free-stream Mach numbers [2,4,6] and four wall
temperature conditions (from adiabatic to very cold walls), emphasising the
choice of the diabatic parameter $\mathit{\Theta}$ (Zhang, Bi, Hussain & She,
J. Fluid Mech., vol. 739, pp. 392-420) to recover a similar flow organisation
at different Mach numbers. We link qualitative observations on flow patterns to
first- and second-order statistics to explain the strong decoupling of
temperature-velocity fluctuations that occurs at reduced wall temperatures and
high Mach numbers. For these cases, we find that the mean temperature gradient
in the near-wall region can reach such a strong intensity that it promotes the
formation of a secondary peak of thermal production in the viscous sublayer,
which is in direct contrast with the monotonic behaviour of adiabatic profiles.
We propose different physical mechanisms induced by wall-cooling and
compressibility that result in apparently similar flow features, such as a
higher peak in the streamwise velocity turbulence intensity, and distinct ones,
such as the separation of turbulent scales.
