This paper considers a problem of area coverage where the objective is to achieve given coverage density by use of multiple mobile agents. We present an ergodicity-based coverage algorithm which enables a centralized feedback control for multiagent system based on radial basis function (RBF) representation of the ergodicity problem and a solution of an appropriately designed stationary heat equation for the potential field. The heat equation uses a source term that depends on the difference between the given goal density distribution and the current coverage density (time average of RBFs along trajectories). The agent movement is directed using the gradient of that potential field. The heat equation driven area coverage has a built-in cooperative behavior of agents which includes collision avoidance and coverage coordination. The algorithm is robust, scalable, and computationally inexpensive.