In the framework of a novel dissipative scheme, we have investigated the quantum dynamics of an oscillating system interacting with two reservoirs with different temperatures trough different time-dependent coupling functions. The reduced density matrix, quantum optical characteristic functions, and (quasi) distribution functions like Husimi, Glauber-Sudarshan and Wigner functions on the phase space of the oscillator are obtained. The problem has been generalized to the case where the oscillator is interacting with (n) distinctive reservoirs, and a quantum current and an effective reservoir is introduced. Finally, the quantum dynamics of a two-level system interacting with two reservoirs has been investigated, and the exact reduced density matrix is obtained.