As the next generation power grid, smart grid is characterized as an informationized system, and demand response is one of its important features to deal with the ever-increasing peak energy usage. However, the supply capacity and required demand make the demand response problem with both spatially and temporally coupled constraints, which, to the best of our knowledge, has not been thoroughly investigated in a distributed manner. The complexity lies in how to guarantee privacy and convergence of distributed algorithms. Aiming at this challenge, in this paper, we first propose a distributed algorithm, which is based on dual decomposition and does not require each user to reveal his/her private information. Then, the convergence analysis is conducted to provide guidance on how to choose the proper step size; through which, we notice that the convergence speed of the subgradient projection method is not fast enough and it is highly dependent on the choice of the step size. Therefore, to increase the convergence rate of the distributed algorithm, we further propose a fast approach based on binary search. Finally, the distributed algorithms are illustrated by numerical simulations and the extensive comparison results validate the better performance of the fast approach.