We consider the channel assignment problem in wireless mesh networks. Due to the limited number of radio interfaces that each node is equipped with, channel assignment must ensure that the interface constraint is obeyed, i.e., the number of different channels assigned to the links incident on a node must be no greater than the number of interfaces the node is equipped with. However, interface constraint may be one of the causes that hinder the performance of some of the existing heuristics. In this paper, we use simulated annealing to solve the channel assignment problem in wireless mesh networks. We propose two neighbor generating approaches that handle the interface constraint in different ways. The first approach starts with an infeasible random solution, and by using the penalty function technique the solution finally converges to a feasible one. The second approach, on the contrary, allows only feasible solutions to be generated during the simulated annealing process. Simulations are conducted that compare our proposed simulated annealing algorithms together with a tabu-based algorithm under different network traffic scenarios. The results show that our algorithms exhibit lower network interference than the tabu-based algorithm.