ESA’s Atmospheric Remote-sensing Infrared Exoplanet Large-survey (ARIEL) mission, due to launch in 2028, will acquire simultaneous visible photometry and near-infrared spectra of ~1000 exoplanets that transit their host stars (Tinneti et al. 2018, Exp. Astron. 46, 135). The infrared molecular bands of many species that are expected to reside in the atmospheres of transiting-exoplanet targets are included in the 1.25–7.8 micron spectral range covered by ARIEL. To investigate the role of chemistry in ARIEL phase-curve observations, we use a two-dimensional (2D) thermal-structure model and pseudo-2D chemical kinetics model to predict the altitude and longitude variation of atmospheric temperatures and constituent abundances at low latitudes on Neptune-class exoplanets that orbit at different distances from their host stars. Our models predict that the low-latitude vertical profiles of temperature and species’ abundances vary significantly with longitude and with planetary equilibrium temperature (Teq). Day-night temperature contrasts are found to increase with increasing planetary Teq. We also find that horizontal transport-induced quenching acts to homogenize species’ abundances with longitude on our Neptune-class exoplanets, similar to what is expected to occur on hot Jupiters (Cooper & Showman 2006, ApJ 649, 1048; Agúndez et al. 2014, A&A 564, A73). Our models have implications with respect to phase-curve observations of Neptune-class exoplanets with ARIEL. For example, we find that that the atmosphere remains near thermochemical equilibrium and that temperature variations dominate phase-curve variations on very hot Neptunes, whereas disequilibrium chemistry is important on cool Neptunes but their emission emission does not vary much with planetary phase. Our models reveal a “sweet spot” in Teq space such that intermediate-temperature Neptunes have phase curves that are affected by both global temperature and abundance variations, revealing interesting atmospheric processes. This sweet spot in Teq shifts to lower temperatures as metallicity is increased, making cool higher-metallicity Neptune-class planets appropriate targets for ARIEL phase-curve observations.