The objective of this paper is to describe a parallel acceleration framework of the additive schwarz waveform relaxation for parabolic problems. The problem is in three space dimension and time. This new parallel domain decomposition algorithm generalizes the Aitken-like Acceleration method of the additive Schwarz algorithm for elliptic problems. Although the standard Schwarz Waveform Relaxation algorithm has a linear rate of convergence and low numerical efficiency, it is beneficent to cache use and scales with the memory. The combination with the Aitken-like Acceleration method transforms the Schwarz algorithm into a direct solver for the heat operator. This solver combines all in one the load balancing, the efficiency, the scalability and the fault tolerance features which make it suitable for grid environments.