Short time approximation is developed for system-environmental bath mode interactions involving a general non-Hermitian system operator Λ, and its conjugate, Λ^†, in order to evaluate onset of decoherence at low temperatures in quantum systems interacting with environment. The developed approach is complementary to Markovian approximations and appropriate for evaluation of quantum computing schemes. Example of a spin system coupled to a bosonic heat bath via Λ∝σ_- is worked out in detail.