  Numerical and closed-form analytic expressions for plasmon dispersion
relations and rates of dissipation are first obtained at finite-temperatures
for free-standing gapped graphene. These closed-system results are generalized
to an open system with Coulomb coupling of graphene electrons to an external
electron reservoir. New plasmon modes, as well as new plasmon dissipation
channels, are found in this open system, including significant modifications
arising from the combined effect of thermal excitation of electrons and an
energy bandgap in gapped graphene. Moreover, the characteristics of the new
plasmon mode and the additional plasmon dissipation may be fully controlled by
adjusting the separation between the graphene layer from the surface of a thick
conductor. Numerical results for the thermal shift of plasmon frequency in a
doped gapped graphene layer, along with its sensitivity to the local
environment, are demonstrated and analyzed. Such phenomenon associated with the
frequency shift of plasmons may be applied to direct optical measurement of
local electron temperature in transistors and nanoplasmonic structures.
