0_3499 We present recent ab-intio simulation results for matter strongly dressed by optical cavities. Our focus will be on the relevance of classical and quantum features emergent from the vibrational strong coupling to the vacuum field fluctuations at finite temperature. The role and description of cavity induced non-canoncial equilibrium condition for chemical systems, as well as the relevance of thermal baths for local and collective features will be explored and consequences for the future development of ab-initio methods will be derived.