The mechanical properties of anisotropic carbons such as the pyrocarbon (pyC) matrices in C/C composites remain poorly documented, especially at elevated temperatures where these materials find most of their applications. We provide here a comprehensive molecular dynamics investigation of the high temperature – up to 4000 K – elastic behavior of six nanoscale pyC models in the context of fast temperature increases, not allowing for major structural modifications such as graphitization. We show that the structure of the most anisotropic and less disordered carbons, like the rough laminar (RL) pyC, is mostly not affected by annealing at the nanosecond timescale, aside from healing unstable defects like two-coordinated atoms at graphene edges. Conversely, highly disordered and less anisotropic carbons like the smooth laminar (SL) pyC show some significant rearrangements at grain boundaries and the development of some limited microporosity. The elastic constants of all highly anisotropic models moderately decrease with increasing temperature, somehow similarly to what is observed for graphite. Elastic constants of the SL pyC show a stronger decrease at high temperature, due to the decrease in density even though all models retain an important degree of stiffness up to 4000 K.