We discuss parallel performance of h-type Adaptive Mesh Refinement (AMR) developed for the high-order spectral element solver Nek5000 within CRESTA project. AMR is a desired feature of the future simulation software, as it gives possibility to increase the accuracy of numerical simulations at minimal computational cost by resolving particular region of the domain. At the same time it increases complexity of the communication pattern and introduces load imbalance, that can have negative effect on the code scalability. In this work we concentrate on the parallel performance of different tools required by AMR and the resulting algorithm limitations. Our implementation is based on available libraries for parallel mesh management (p4est) and partitioning (ParMetis) that provide necessary information for grid refinement/coarsening and redistribution performed within nonconforming version of Nek5000. For simplicity we consider advection-diffusion problem instead of the full Navies-Stokes equations and study both strong and weak scalability for the convected-cone problem. It is a synthetic test case allowing to test AMR with frequent dynamic mesh adjustments.