  Lorentz and CPT symmetries may be violated in new physics that emerges at
very high energy scale, i.e., at the Planck scale. The differential cross
section of the M\"oller scattering, due to Lorentz violation at finite
temperature is calculated. Lorentz-violating effects emerge from an interaction
vertex due to a CPT-odd nonminimal coupling in the covariant derivative. The
finite temperature effects are determined using the Thermo Field Dynamics (TFD)
formalism.
