  The discovery of a planet orbiting around Proxima Centauri, the closest star
to the Sun, opens new avenues for the remote observations of the atmosphere and
surface of an exoplanet, Proxima b. To date, three-dimensional (3D) General
Circulation Models (GCMs) are the best available tools to investigate the
properties of the exo-atmospheres, waiting for the next generation of space and
groundbased telescopes. In this work, we use the PlanetSimulator (PlaSim), an
intermediate complexity 3D GCM, a flexible and fast model, suited to handle all
the orbital and physical parameters of a planet and to study the dynamics of
its atmosphere. Assuming an Earth-like atmosphere and a 1:1 spin/orbit
configuration (tidal locking), our simulations of Proxima b are consistent with
a day-side open ocean planet with a superrotating atmosphere. Moreover, because
of the limited representation of the radiative transfer in PlaSim, we compute
the spectrum of the exoplanet with an offline Radiative Transfer Code with a
spectral resolution of 1 nm. This spectrum is used to derive the thermal phase
curves for different orbital inclination angles. In combination with
instrumental detection sensitivities, the different thermal phase curves are
used to evaluate observation conditions at ground level (e.g., ELT) or in space
(e.g., JWST). We estimated the exposure time to detect Proxima b (assuming an
Earth-like atmosphere) thermal phase curve in the FIR with JWST with
signal-to-noise ratio $\simeq$1. Under the hypothesis of total noise dominated
by shot noise, neglecting other possible extra contribution producing a noise
floor, the exposure time is equal to 5 hours for each orbital epoch.
