In this letter, we study strong structural controllability of linear time varying network systems that change network topology and edge weights with time. We derive graph based necessary and sufficient conditions for strong structural controllability of temporal networks. We provide a polynomial time algorithm to compute the dimension of the strong structurally controllable subspace of a temporal network. This allows us to verify whether a given set of inputs leads to a controllable system for all choices of numerical realizations. Next, we show that the problem of finding a minimum size input for strong structural controllability of temporal networks is an NP-hard problem. We propose a greedy heuristic algorithm to optimize the size of the input set for strong structural controllability of temporal networks and compare the performance of the greedy algorithm with the optimum solution through simulations. © 2017 IEEE.