The Duschinsky effect has been shown to be significant in spectroscopy and dynamics of molecules that involve the pi-pi* transitions. In this paper, we present a derivation of exact expressions for optical absorption and radiationless transitions in polyatomic molecules with displaced-distorted-rotated harmonic potential surfaces. In the formulation, we take into account the temperature effect exactly. The application of this new formulation is demonstrated for ethylene and allene, where the Duschinsky effect in the first singlet excited electronic state is very strong.