Before revision:  While limited speedup from the time parallelization is shown to be possible, load balancing is identified as an important issue in the application of Pararealwith implicit integrators to complex PDEs .
After revision:  It is confirmed that anisotropies in the domain and jumps in diffusion coefficients only have a minor impact on Parareal's convergence. The influence of load imbalances in time due to differences in number of iterations required by the spatial solver as well as spatio-temporal weak scaling is discussed .