Three‐dimensional woven carbon‐fiber reinforced polymers (3D‐CFRP) are being increasingly used for blades in rotordynamical systems as turbine fans, shafts as well as disc brake rotors. By using dynamic mixed finite‐element methods, these materials can be simulated as anisotropic continua with non‐isothermal behaviour in the matrix as well as the fiber material. Therefore, we present a novel dynamic mixed finite‐element method which is variational‐based and capable to simulate these materials. This dynamic mixed finite‐element method preserves each basic balance law emanating from the variational principle exact in a discrete setting. We demonstrate this physically‐consistent simulation behaviour by using dynamic simulations of a disc brake rotor and a rotating pipe subject to thermal and mechanical loads.