The fluctuation-dissipation theorem, one of the central theorems in thermal dynamics, breaks down in out-of-equilibrium systems. The idea of effective temperature coming from the extensions of that theorem has been recently introduced to study glasses and has proved to be a key concept for out-of-equilibrium systems. Gene networks involve stochastic chemical kinetics and are far from equilibrium. This leads us to try to use the notion of effective temperature to study them. To develop this idea, we study a simple birth-death process and a general two-species interacting process using the language of effective temperature. Furthermore, a model of a nonregulatory gene is studied as an example. The effective temperature may serves as an alternative and somewhat more fundamental language to describe the intrinsic-extrinsic noise distinction that has already provided a tool for qualifying gene networks.