Intermittent renewable energy, such as solar and wind, brings uncertainty into the grid. To increase their contribution into the energy mix, load management solutions are necessary to correct the resulting typical mismatches between generation and demand. This can be achieved rather effectively with thermostatic loads such as space heaters or water heaters by considering them as means of storage. This article proposes a mean field game-based controller to provide load flexibility into the grid using a multi-layer water heater model. A uniform local state feedback law is used to track the temperature trajectory specified by an aggregator for the group of controlled devices. The law is computed via a near fixed-point algorithm. A scheduling problem for the desired mean water heater target temperatures over a time horizon is formulated to find the maximum flexibility available from the group of loads while maintaining the typical post-control load oscillations within predefined bounds over a fixed time period. The solution of the scheduling problem is obtained by solving a linear optimization problem with upper and lower bounds on the power drawn by the group to converge to an acceptable mean temperature schedule.