High Mach-number compressible flows with heat release are inherently more complicated than incompressible flows due to, among other reasons, the activation of the thermal energy mode. Such flow fields can experience significant fluctuations in density, temperature, viscosity, conductivity and specific heat, which affect velocity and pressure fluctuations. Furthermore, the flow field cannot be assumed to be dilatation-free in high Mach numbers and even in low Mach-number flows involving combustion, or in boundary layers on heated walls. The main issue in these high-speed and highly-compressible flows is the effect of thermal gradients and fluctuations on turbulence. The thermal field has various routes through which it affects flow structures of compressible turbulence. First, it has direct influence through pressure, which affects turbulence via pressure-strain correlation. The indirect effects of thermal fields on compressible turbulence are through the changes in flow properties. The high temperature gradients alter the transport coefficient and compressibility of the flow. The objective of this work is to answer the following questions: How do temperature fluctuations change the compressible flow structure and energetics? How does compressibility in the flow affect the non-linear pressure redistribution process? What is the main effect of spatial transport-coefficient variation? We perform direct numerical simulations (DNS) to answer the above questions. The investigations are categorized into four parts: 1) Turbulent energy cascade and kinetic-internal energy interactions under the influence of temperature fluctuations; 2) Return-to-isotropy of anisotropic turbulence under the influence of large temperature fluctuations; 3) The effect of turbulent Mach number and dilatation level on small-scale (velocity-gradient) dynamics; 4) The effect of variable transport-coefficients (viscosity and diffusivity) on cascade and dissipation processes of turbulence. The findings lead to a better understanding of temperature fluctuation effects on non-linear processes in compressible turbulence. This improved understanding is expected to provide direction for improving second-order closure models of compressible turbulence.