It is commonly accepted that shear waves do not propagate in a liquid medium. The shear wave energy is supposed to dissipate nearly instantaneously. This statement originates from the difficulty to access “static” shear stress in macroscopic liquids. In this paper, we take a different approach. We focus on the stability of the thermal equilibrium while the liquid (glycerol) is submitted to a sudden shear strain at sub-millimeter scale. The thermal response of the deformed liquid is unveiled. The liquid exhibits simultaneous and opposite bands up to about -0.04 to +0.04°C temperature variation, while keeping the global thermal balance unchanged. The sudden thermal changes and the long thermal relaxation highlight the ability of the liquid to convert the step strain energy in non-uniform thermodynamic states. The thermal effects depend nearly linearly on the amplitude of the deformation supporting the hypothesis of a shear wave propagation (elastic correlations) extending up to several hundreds micrometers. This new physical effect can be explained in terms of the underlying phonon physics of confined liquids, which unveils a hidden solid-like response with many similarities to glassy systems.