  We have derived algebraic, analytic expressions for the chemical potential
without any restriction on temperature for all types of doped, or extrinsic,
gapped Dirac cone materials including gapped graphene, silicene, germanene and
single-layer transition metal dichalcogenides. As an important intermediate
step of our derivations, we have established a reliable piecewise-linear model
for cal- culating the density-of-states in molybdenum disulfide, showing good
agreement with previously obtained numerical results. For the spin- and
valley-resolved band structure, we obtain an additional decrease of the
chemical potential due to thermally induced doping of the upper subband at
finite temperature. It has been demonstrated that since the symmetry between
the electron and hole states in $MoS_2$ is broken, the chemical potential could
cross the zero-energy level at sufficiently high temperature. These results
allow us to investigate the collective properties, polarizability, plasmons and
their damping. Emphasis is placed on low temperatures, when initial electron
doping plays a crucial role. We clearly demonstrated the contribution of the
initial doping to the finite-temperature collective properties of the
considered materials.
