Chromium trihalides are layered and exfoliable semiconductors and exhibit unusual magnetic properties with a surprising temperature dependence of the magnetization. By analyzing the evolution of the magnetocrystalline anisotropy with temperature in chromium iodide CrI3, we find it strongly changes from Ku=300±50kJ/m3 at 5K to Ku=43±7kJ/m3 at 60K, close to the Curie temperature. We draw a direct comparison to CrBr3, which serves as a reference, and where we find results consistent with literature. In particular, we show that the anisotropy change in the iodide compound is more than 3 times larger than in the bromide. We analyze this temperature dependence using a classical model, showing that the anisotropy constant scales with the magnetization at any given temperature below the Curie temperature, indicating that the temperature dependence can be explained by a dominant uniaxial anisotropy where this scaling results from local spin clusters having thermally induced magnetization directions that deviate from the overall magnetization.