We propose solutions for assignment of physical tasks to heterogeneous agents when the costs of the tasks change over time. We assume tasks have a natural growth rate which is counteracted by the work applied by the agents. As the future cost of a task depends on the agents allocation, reasoning must be both spatial and temporal to effectively minimize the growth so tasks can be completed. We present optimal solutions for two general classes of growth functions and heuristic solutions for other cases. Empirical results are given in RoboCup Rescue for agents with different capabilities.