We have investigated the thermomechanical structure in strongly chaotic non‐Newtonian thermal convection for both base‐heated and internally‐heated systems. Temperature can build up in stagnant regions and a non‐Newtonian mantle can tolerate less internal‐heating. Viscosity fields of strongly chaotic regime show a granular structure. The horizontal spectra of viscosity fluctuations obey a power‐law and yield a fractal dimension of 1.6 to 1.8 for the isoviscosity lines, providing evidence for two‐dimensional turbulence. Long wavelength viscosity variations are smoothed out by the turbulent non‐Newtonian flows.