We consider a model for heterogeneous gene regulatory networks that is an "annealed approximation" of Kauffmann's (1969) original random Boolean networks. In this model, genes are represented by the nodes of a random directed graph $G_n$ on $n$ vertices with specified degree distribution, and the interactions among the genes are approximated by an appropriate threshold contact process (in which a vertex with at least one occupied in-neighbor at time $t$ will be occupied at time $t+1$ with probability $q$, and vacant otherwise) on $G_n$. We characterize the order-chaos phase transition curve for the threshold-contact process on $G_n$ segregating the chaotic and ordered random Boolean networks.