It depends on a lot of factors like the individual melting temperatures of the nanoparticles and the matrix, their thermal conductivity, heat capacity etc. As you rise the temperature, if the thermal conductivity is not very small, both the nanoparticles and the matrix suffer from equal elevation in temperature.
Of course, the melting temperature for the composite might not be a single temperature like an alloy. Rather the nanoparticles and matrix might melt at different temperatures, depending on their separate melting temperature, which should get modified by a factor in the composite environment.
In addition, I will add that the nanoparticles in the composite have a large contact surface with the main matrix lattice. Therefore, the influence of surface tension on this surface is great. In my experience, it can shift the melting temperature of nanoinclusions, compared to bulk matter, by up to 100 degrees.