A Distributed Constraint Satisfaction Problem (DisCSP) is a constraint satisfaction problem in which variables and constraints are distributed among multiple agents. Various algorithms for solving DisC-SPs have been developed, which are intended for general purposes, i.e., they can be applied to any network structure. However, if a network has some particular structure, e.g., the network structure is scale-free, we can expect that some specialized algorithms or heuristics, which are tuned for the network structure, can outperform general purpose algorithms/heuristics. In this paper, as an initial step toward developing specialized algorithms for particular network structures, we examine variable-ordering heuristics in scale-free networks. We use the classic asynchronous backtracking algorithm as a baseline algorithm and examine the effect of variable-ordering heuristics. First, we show that the choice of variable-ordering heuristics is more influential in scale-free networks than in random networks. Furthermore, we develop a novel variable-ordering heuristic that is specialized to scale-free networks. Experimental results illustrate that our new variable-ordering heuristic is more effective than a standard degree-based variable-ordering heuristic. Our proposed heuristic reduces the required cycles by 30% at the critical point.