A new notion of phase of multi-input multi-output (MIMO) systems was recently defined and studied, leading to new understandings in various fronts including a formulation of small phase theorem, a performance criterion named H-infinity phase sector, and a sectored real lemma, etc. In this paper, we define a new notion of H-2(T) -dissipativity and show the connection between the phase of a multivariable linear time-invariant (LTI) system and the H-2(T) -dissipativity. The H-2(T) -dissipativity, roughly speaking, is dissipativity restricted to the time-domain H-2 space which consists of L-2 signals with only positive frequency components. In addition, by exploiting the newly defined H-2(T) dissipativity, we also study the phase of a feedback system and provide a physical interpretation of the sectored real lemma.