In this paper, we develop a distributed intermittent communication and task planning framework for mobile robot teams. The goal of the robots is to accomplish complex tasks, captured by local linear temporal logic formulas, and share the collected information with all other robots and possibly also with a user. Specifically, we consider situations where the robot communication capabilities are not sufficient to form reliable and connected networks, while the robots move to accomplish their tasks. In this case, intermittent communication protocols are necessary that allow the robots to temporarily disconnect from the network in order to accomplish their tasks free of communication constraints. We assume that the robots can only communicate with each other when they meet at common locations in space. Our distributed control framework jointly determines local plans that allow all robots to fulfill their assigned temporal tasks, sequences of communication events that guarantee information exchange infinitely often, and optimal communication locations that minimize a desired distance metric. Simulation results verify the efficacy of the proposed controllers.