Generating high quality schedules for distributed applications on a Computational Grid is a challenging problem. Some experiments using Simulated Annealing as a scheduling mechanism for a ScaLAPACK LU solver on a Grid are described. The Simulated Annealing scheduler is compared to a Ad-Hoc Greedy scheduler used in earlier experiments. The Simulated Annealing scheduler exposes some assumptions built into the Ad-Hoc scheduler and some problems with the Performance Model being used.