  We apply the operator product expansion (OPE) technique to the decay and
annihilation of heavy particles in a thermal medium with temperature below the
heavy particle mass, m_chi. This allows us to explain two interesting
observations made before: a) that the leading thermal correction to the decay
width of a charged particle is the same multiplicative factor of the
zero-temperature width for a two-body decay and muon decay, and b) that the
leading thermal correction to fermionic dark matter annihilation arises only at
order T^4/m_chi^4. The OPE further considerably simplifies the computation and
factorizes it into model-independent matrix elements in the thermal background,
and short-distance coefficients to be computed in zero-temperature field
theory.
