Membrane inhomogeneity gives rise to a perturbation energy that may be manifested as line tension between regions of different compositions. Here we calculate the perturbation energy of a phase-separated fluid membrane composed of domains embedded in a continuous phase and relate it to the line tension in the system. We find that the effective line tension due to the thickness mismatch between the phases varies nonmonotonically as a function of the domain size and spacing when those decrease below about 20 nm. Although we find that the characteristic time scale for domain coalescence increases with domain size, the coalescence time for domains on the order of 25 to 50 nm may be as long as several days. The time scale for domain coalescence is found, quite surprisingly, to be maximal when the bending and area moduli of the domain and continuous phase are similar and to decrease when one phase is stiffer than the other. Domain stability is also found to vary as a function of spacing; as a result, small domains on the order of 5 nm become unstable and tend to coalesce when the domain-phase area fraction increases above 0.5, whereas larger domains on the order of 50 nm become unstable only when the area fraction increases above 0.8.