  Hyperspectral imaging at cryogenic temperatures is used to investigate
exciton and trion propagation in MoSe$_2$ monolayers encapsulated with
hexagonal boron nitride (hBN). Under a tightly focused, continuous-wave laser
excitation, the spatial distribution of neutral excitons and charged trions
strongly differ at high excitation densities. Remarkably, in this regime the
trion distribution develops a halo shape, similar to that previously observed
in WS2 monolayers at room temperature and under pulsed excitation. In contrast,
the exciton distribution only presents a moderate broadening without the
appereance of a halo. Spatially and spectrally resolved luminescence spectra
reveal the buildup of a significant temperature gradient at high excitation
power, that is attributed to the energy relaxation of photoinduced hot
carriers. We show, via a numerical resolution of the transport equations for
excitons and trions, that the halo can be interpreted as thermal drift of
trions due to a Seebeck term in the particle current. The model shows that the
difference between trion and exciton profiles is simply understood in terms of
the very different lifetimes of these two quasiparticles.
