As part of a continuing study of the mechanical behavior of materials with temperature‐dependent properties, dynamic responses of an ideal viscous material are considered. An electric analog circuit containing thermistors and ideal inductors is presented. The characteristics of this circuit simulate the highly nonlinear characteristics of the model of the material. The experiments show how the conversion of mechanical work to heat can lead to stress and time‐dependent apparent viscosities and to thermal instability in velocity‐driven Couette flow. When the boundary velocity is sinusoidal, the heating can lead to the appearance of a pseudo elasticity as well as to thermal instability. The thermal stability of the system is shown to depend on the frequency as well as the amplitude of the excitation. A group of similarity parameters are described which are ratios of characteristic times for heating, velocity diffusion, thermal diffusion, and loading. These provide a description of the model mechanical experiment and make the connection with the electrical analog.