In the proximity of melting transitions of artificial and biological membranes fluctuations in enthalpy, area, volume and concentration are enhanced. This results in domain formation, a change of the elastic constant, changes in permeability and longer relaxation processes. In this study we used pressure perturbation calorimetry to investigate the time scale of domain formation processes after a jump into the melting transition regime of artificial lipid membranes. The studies were performed on single-component large unilamellar and multilamellar vesicle systems with and without the addition of small molecules such as general anesthetics, neurotransmitters and antibiotics. These drugs interact with membranes and affect melting points and profiles. In all systems we found that heat capacity and relaxation times are related to each other in a simple manner. The maximum relaxation time depends on the cooperativity of the heat capacity profile and decreases with a broadening of the transition. For this reason the influence of a drug on the time scale of domain formation processes can be understood on the basis of their influence on the heat capacity profile. This allows estimations of the time scale of domain formation processes in biological membranes.