Magnetization as a function of temperature calculated with Monte Carlo techniques is compared to experimental results of Fe stripes grown on vicinal Cu(111) surfaces. The stripes are step decorations grown with molecular beam epitaxy (MBE), are 1-2 monolayers thick, and display perpendicular magnetization. The atomic parameters are determined from fully relativistic electronic structure calculations. The moments are found to be 2.57 μ_B, with some variation due to film thickness, and uniaxial anisotropy of 40 μRy/atom for Fe atoms facing vacuum. The Heisenberg model extended to include crystalline anisotropy as well as dipole-dipole interactions is considered for two different values of the exchange constant: J = 20 and 2 meV. Under a large applied field (4000 G), the calculated saturation magnetization falls slowly from 507 emu/cm³ with an increase in temperature until it falls rapidly around 600 K, after which a more modest fall off with an increase in temperature is observed. For larger J the rapid change occurs for higher temperatures. The importance of disorder in the height and width of the stripes is investigated by generating stripe geometries with a model that incorporates nucleation and growth of Fe particles at step edges under the constraint of constant deposition from MBE. The primary effect of disorder in the stripes is to reduce the saturated magnetization at lower temperatures.