First, by TCE I assume that you are referring to Thermal Coefficient of Expansion. Is that right?
I am not quite sure what you have mind with the TNM term, however. I use TNM when talking about the Three Network Model. What do you mean by TNM?
The easiest viscoelastic material model to use is a linear viscoelasticity model. To use that model you need both the elastic part of the response, and information about the viscous response. In your case if sounds like you know the viscosity, and hence you can calibrate a one-term Prony series to your viscosity data set. If you then combine that with a hyperelastic material model then you will have a valid linear viscoelasticity model.
Best of luck,
Jorgen Bergstrom, Ph.D.