Shape, stability and chemical ordering patterns of CuNi nanoalloys are studied as a function of size, composition and temperature. A new parametrization of an atomistic potential for CuNi is developed on the basis of ab initio calculations. The potential is validated against experimental bulk properties, and ab initio results for nanoalloys of sizes up to 147 atoms and for surface alloys. The potential is used to determine the chemical ordering patterns of nanoparticles with diameters of up to 3 nm and different structural motifs (decahedra, truncated octahedra and icosahedra), both in the ground state and in a wide range of temperatures. The results show that the two elements do not intermix in the ground state, but there is a disordering towards solid-solution patterns in the core starting from room temperature. This order-disorder transition presents different characteristics in the icosahedral, decahedral and fcc nanoalloys.