Epitaxial layers of wurtzite-phase Al1-xInxN, similar to 120 nm thick with (0 0 0 1) orientation, were grown by metal organic chemical vapour deposition on GaN buffer layers at setpoint temperatures between 760 and 840 degrees C. For growth temperatures >= 800 degrees C, the AlInN layers grew with uniform composition, pseudomorphic with the underlying GaN buffer layer. In the temperature range studied, the InN fractions are a linear function of the setpoint temperature and straddle the near-lattice-match composition around Al0.83In0.17N. Lowering the growth temperature to 760 degrees C caused a compositional grading, a marked change in surface morphology, and a reduction in AlInN crystal quality. The resulting AlInN layer consists of a compressively strained interfacial layer with a composition of Al0.76In0.24N and a mostly relaxed near-surface layer with a composition of A10.811no.19N. Atomic force microscopy suggests that a transition to a three-dimensional growth mode accompanies the structural relaxation and change in composition.