An effective large-scale model of interacting boson gas at low temperatures is constructed from first principles. The starting point is the generating function of time-dependent Green functions at finite temperature. The perturbation expansion is worked out for the generic case of finite time interval and grand-canonical density operator with the use of the S-matrix functional for the generating function. Apparent infrared divergences of the perturbation expansion are pointed out. Regularization via attenuation of propagators is proposed and the relation to physical dissipation is studied. Problems of functional-integral representation of Green functions are analyzed. The proposed large-scale model is explicitly renormalized at the leading order.