Context. The single rapidly-rotating G0 giant 31 Comae has been a puzzle because of the absence of photometric variability despite its strong chromospheric and coronal emissions. As a Hertzsprung-gap giant, it is expected to be at the stage of rearranging its moment of inertia, hence likely also its dynamo action, which could possibly be linked with its missing photospheric activity. Aims. Our aim is to detect photospheric activity, obtain the rotation period, and use it for a first Doppler image of the star's surface. Its morphology could be related to the evolutionary status. Methods. We carried out high-precision, white-light photometry with the MOST satellite, ground-based Strömgren photometry with automated telescopes, and high-resolution optical echelle spectroscopy with the new STELLA robotic facility. Results. The MOST data reveal, for the first time, light variations with a full amplitude of 5 mmag and an average photometric period of 6.80 ± 0.06 days. Radial-velocity variations with a full amplitude of 270 m s −1 and a period of 6.76 ± 0.02 days were detected from our STELLA spectra, which we also interpret as due to stellar rotation. The two-year constancy of the average radial velocity of +0.10 ± 0.33 km s −1 confirms the star's single status, as well as the membership in the cluster Melotte 111. A spectrum synthesis gives T eff = 5660 ± 42 K, log g = 3.51 ± 0.09, and [Fe/H] = −0.15 ± 0.03, which together with the revised Hipparcos distance, suggests a mass of 2.6 ± 0.1 M and an age of ≈540 Myr. The surface lithium abundance is measured to be nearly primordial. A detection of a strong He i absorption line indicates nonradiative heating processes in the atmosphere. Our Doppler images show a large, asymmetric polar spot, cooler than T eff by ≈1600 K, and several small low-to-mid latitude features that are warmer by ≈300-400 K and are possibly of chromospheric origin. We computed the convective turnover time for 31 Com as a function of depth and found on average τ C ≈ 5 days. Conclusions. 31 Com appears to be just at the onset of rapid magnetic braking and Li dilution because its age almost exactly coincides with the predicted onset of envelope convection. That we recover a big polar starspot despite the Rossby number being larger than unity, and thus no efficient (envelope) dynamo is expected, leads us to conclude that 31 Com still harbors a fossil predominantly poloidal magnetic field. However, the increasing convective envelope may have just started an interface dynamo that now is the source of the warm surface features and the corresponding UV and X-ray emission.