The magnetic domain structure of the Fe double-layer on W(1 1 0) is investigated using a variable-temperature scanning tunneling microscope. At low temperature the well-known periodic magnetic stripe domain structure is identified via the observation of domain walls. This is done with a non-spin-polarized tip by taking advantage of a spin-orbit coupling effect. At higher temperature a reorientation to an in-plane easy axis is observed. The spin reorientation temperature is found to be coverage-dependent and it is determined for samples with a coverage of 1.5-2.2 atomic layers of Fe on W(1 1 0).