Second-stage laser cooling of thulium atoms at the 530.7 nm transition with a natural linewidth of 350 kHz offers an interesting possibility to study different regimes of a magneto-optical trap (MOT). The intermediate value of the spectral linewidth of the cooling transition allows the observation of three distinct regimes depending on the intensity and detuning of the cooling beams, namely, the "bowl-shaped" regime when light pressure force competes with gravity, the "double structure" regime with interplay between the Doppler and polarization-gradient (sub-Doppler) cooling, and the "symmetric" regime when Doppler cooling dominates over sub-Doppler cooling and gravity. The polarization-gradient cooling manifests itself by a two-temperature momentum distribution of atoms resulting in a double-structure of the spatial MOT profile consisting of a cold central fraction surrounded by a hot halo. We studied the double structure regime at different saturation parameters and compared observations with calculations based on semiclassical and quantum approaches. The quantum treatment adequately reproduces experimental results if the MOT magnetic field is properly taken into account.