Viscoelasticity describes the ability of a material to possess both elasticity and viscosity. Viscoelastic materials, such as rubbers, possess a limited operational temperature range (for example, for silicone rubber it is -55 degrees to 300 degrees C), above which the material breaks down and below which the material undergoes a glass transition and hardens. We created a viscoelastic material composed from a random network of long interconnected carbon nanotubes that exhibited an operational temperature range from -196 degrees to 1000 degrees C. The storage and loss moduli, frequency stability, reversible deformation level, and fatigue resistance were invariant from -140 degrees to 600 degrees C. We interpret that the thermal stability stems from energy dissipation through the zipping and unzipping of carbon nanotubes at contacts.