We study compressive shock waves in a nonisothermal power-law fluid within Rational Extended Thermodynamics, with viscous stress as an independent relaxing field. The energy balance couples viscous heating to temperature-dependent rheology, and the traveling-wave problem reduces to a scalar equation. Under explicit stability and Hugoniot-convexity assumptions, we establish that the upstream state is the global minimum of the relevant characteristic speed along the compressive branch. This nontrivial ordering result, which requires controlling the thermal coupling absent in the isothermal model, ensures continuous shock profiles below a critical speed and implies that admissible piecewise-smooth profiles above it contain a subshock. We also exclude nontrivial compressive profiles at constant temperature. The flow-index thresholds m=2 for weak shocks and m=1 near subshock onset, known from the isothermal theory, persist in the nonisothermal setting, together with their critical thickness exponents. Their amplitudes and the critical speed, however, depend on the constitutive functions. Numerical examples illustrate these results without material-specific calibration.
