The evolution of a magnetic domain structure induced by temperature and magnetic field is reported in silicondoped yttrium iron garnet (YIG) films with perpendicular anisotropy. During a cooling-down procedure from 300 K to 7 K, a 20% change in the domain width is observed, with the long tails of the stripes being shortened and the twisting stripes being straightened. Under the influence of the stray field of a barium ferrite, the garnet presents an interesting domain structure, which shows an appearance of branching protrusions. The intrinsic mechanisms in these two processes are also discussed.