We study the thermodynamic properties of solutions of the physically gelling poly(N-isopropylacrylamide-2-hydroxyethyl methacrylate) [poly(NIPPAm-HEMA)]. We construct its phase diagram and characterize its kinetics of phase separation. This material belongs to a class of thermosensitive, "smart" polymers, that exhibit complex phase behavior. The copolymer studied is liquid at low temperatures and undergoes phase separation near 28 °C, with negligible dependence on concentration. Above the transition temperature we observe coexistence between a polymer-dilute solution and a gel. We show that, upon quick heating, liquid solutions form a homogeneous gel that phase separates (shrinks) from a dilute polymer solution. We find that the evolution of the gel volume fraction is well described by a double exponential decay, indicating the presence of two shrinking regimes in a close parallel to the behavior of chemically cross-linked gels. The first stage is characterized by quick water ejection. In the second stage, slower shrinking is observed associated with internal reorganization of the polymers that allows the creation of gel-forming contacts.