We study the nonlinear, nonlocal dynamics of two-dimensional vesicles in a time-dependent, incompressible viscous flow at a finite temperature. We discuss two problems: (1) a novel phase-treading dynamics in a shear flow, which is induced by the phase decomposition of a lipid mixture; (2) a transient wrinkling dynamics in an extension flow, which is induced by a negative surface tension when the flow direction is reversed. We compute this problem using a stochastic immersed boundary approach and find that thermal fluctuations actually have the ability to attenuate variability of the characteristic wavelength of wrinkling by exciting more wrinkling modes.

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