Over the past decade, observations of giant exoplanets (Jupiter-size) have provided key insights into their atmospheres, but the properties of lower-mass exoplanets (sub-Neptune) remain largely unconstrained because of the challenges of observing small planets. Numerous efforts to observe the spectra of super-Earths--exoplanets with masses of one to ten times that of Earth--have so far revealed only featureless spectra. Here we report a longitudinal thermal brightness map of the nearby transiting super-Earth 55 Cancri e (refs 4, 5) revealing highly asymmetric dayside thermal emission and a strong day-night temperature contrast. Dedicated space-based monitoring of the planet in the infrared revealed a modulation of the thermal flux as 55 Cancri e revolves around its star in a tidally locked configuration. These observations reveal a hot spot that is located 41 ± 12 degrees east of the substellar point (the point at which incident light from the star is perpendicular to the surface of the planet). From the orbital phase curve, we also constrain the nightside brightness temperature of the planet to 1,380 ± 400 kelvin and the temperature of the warmest hemisphere (centred on the hot spot) to be about 1,300 kelvin hotter (2,700 ± 270 kelvin) at a wavelength of 4.5 micrometres, which indicates inefficient heat redistribution from the dayside to the nightside. Our observations are consistent with either an optically thick atmosphere with heat recirculation confined to the planetary dayside, or a planet devoid of atmosphere with low-viscosity magma flows at the surface.