We demonstrate that the temperature and doping dependencies of the photoluminescence (PL) spectra of a doped MoS2 monolayer have several peculiar characteristics defined by the trion radiative decay. While only zero-momentum exciton states are coupled to light, radiative recombination of non-zero momentum trions is also allowed. This leads to an asymmetric broadening of the trion spectral peak and redshift of the emitted light with increasing temperature. The lowest energy trion state is dark, which is manifested by the sharply non-monotonic temperature dependence of the PL intensity. Our calculations combine the Dirac model for the single-particle states, with parameters obtained from the first-principles calculations, and the direct solution of the three-particle problem within the Tamm–Dancoff approximation. The numerical results are well captured by a simple model that yields analytical expressions for the temperature dependencies of the PL spectra.