In principal in order to obtain elastic constants you need to apply force and measure the deformation that this force causes. If we want to obtain the bending elasticity of lipid vesicle we need a force with a very small power. In the case of thermally induced shape fluctuations as a force we use the Brownian (thermal) motion of water molecules, bombarding the membrane. This force is stochastic (we do not know its instant value), but the mean value of it is proportional to the temperature. As a result of this stochastic bombardment the lipid vesicle deforms (changes its shape or fluctuates). We acquire a big amount of pictures of fluctuating vesicle in order to get the mean value of the deformation that our force causes. To extract mean we need to have stationary conditions over the time, so the mean is taken, that is why it is really important to have constant temperature throughout the experiment.
If only measured at one temperature, how would it be possible to draw a conclusion with “thermally induced shape fluctuations”?