We study the problem of scheduling repetitive real-time tasks with the Earliest Deadline First (EDF) policy that can guarantee the given maximal temperature constraint. We show that the traditional scheduling approach, i.e., to repeat the schedule that is feasible through the range of one hyper-period, does not apply any more. Then, we present necessary and sufficient conditions for real-time schedules to guarantee the maximal temperature constraint. Based on these conditions, a novel scheduling algorithm is proposed for developing the appropriate schedule that can ensure the maximal temperature guarantee. Finally, we use experiments to evaluate the performance of our approach.