Context. Current observation techniques are able to probe the atmosphere of some giant exoplanets and get some clues about their atmospheric composition. However, the chemical compositions derived from observations are not fully understood. For instance, the CH 4 /CO abundance ratio is often inferred to be different from the value that has been predicted by chemical models. Recently, the warm Neptune GJ 3470b has been discovered, and because of its close distance from us and high transit depth, it is a very promising candidate for follow-up characterisation of its atmosphere. Aims. We study the atmospheric composition of GJ 3470b to compare to the current observations of this planet and to prepare for future ones but also to understand the chemical composition of warm (sub-)Neptunes as a typical case study. The metallicity of such atmospheres is totally uncertain and are likely to vary to values up to 100× solar. We explore the space of unknown parameters to predict the range of possible atmospheric compositions. Methods. We use a one-dimensional chemical code to compute a grid of models with various thermal profiles, metallicities, eddy diffusion coefficient profiles, and stellar UV incident fluxes. Thanks to a radiative transfer code, we then compute the corresponding emission and transmission spectra of the planet and compare them with the observational data already published. Results. Within the parameter space explored we find that methane is the major carbon-bearing species in most cases. We, however, find that for high metallicities with a sufficiently high temperature, the CH 4 /CO abundance ratio can become lower than unity, as suggested by some multiwavelength photometric observations of other warm (sub-)Neptunes, such as GJ 1214b and GJ 436b. As for the emission spectrum of GJ 3470b, brightness temperatures at infrared wavelengths may vary between 400 and 800 K depending on the thermal profile and metallicity. Conclusions. Combined with a hot temperature profile, a substantial enrichment in heavy elements by a factor of ≥100 with respect to the solar composition can shift the carbon balance in favour of carbon monoxide at the expense of methane. Nevertheless, current observations of this planet do not allow us yet to determine which model is more accurate.