The dataset contains data on the motion and distribution of lipid domains on the membrane of giant unilamellar vesicles in thermal gradients. Each compressed folder contains .tiff images of the fluorescence microscopy data for phase separated vesicles, displayed as Matlab plots with axes labelled in pixels. Each pixel is equal to 0.145 micrometers. There is one compressed folder including the data for each figures 1C, 2B, 2C, 2D, and 6B. As well as images used to track the domains for Fig. 6A. Please refer to the paper for further details. Images are given for the hot and cold caps of vesicles at time t =xmin i.e. folder “t 0min cold” contains images of the cold side of vesicles in a thermal gradient after 0 minutes. The data in the manuscript are obtained from an average of e.g. the domain spacing, domain number or area fraction of white domains for each vesicle in the corresponding folder.