Short-period (<50 day), low-mass (< 10 M⊕) exoplanets are abundant, and the few of them whose radius and mass have been measured already reveal a diversity in composition. Some of these exoplanets are found on eccentric orbits and are subjected to strong tides that affect their rotation and result in significant tidal heating. Within this population, some planets are likely to be depleted in volatiles and have no atmosphere. We modeled the thermal emission of these super Mercuries to study the signatures of rotation and tidal dissipation on their infrared lightcurve. We computed the time-dependent temperature map on the surface and in the subsurface of the planet and the resulting disk-integrated emission spectrum received by a distant observer for any observation geometry. We calculated the illumination of the planetary surface for any Keplerian orbit and rotation. We included the internal tidal heat flow, vertical heat diffusion in the subsurface and generated synthetic lightcurves. We show that the different rotation periods predicted by tidal models (spin-orbit resonances, pseudo-synchronization) produce different photometric signatures, which are observable provided that the thermal inertia of the surface is high, as for solid or melted rocks (but not regolith). Tidal dissipation can also directly affect the lightcurves and make the inference of the rotation more difficult or easier depending on the existence of hot spots on the surface. Infrared lightcurve measurement with the James Webb Space Telescope and EChO can be used to infer exoplanets' rotation periods and dissipation rates and thus to test tidal models. This data will also constrain the nature of the (sub)surface by constraining the thermal inertia.