That's a really good question!
Right off, I don't think you would see two melting points. The reason being that you would at the very least see a lower melting point. Colligative properties dictate this observation.
You do have two electronically different compounds, yet they would be extremely similar when discussing physical properties overall.
So, my guess and this is just a guess, is that you would see a slightly lower melting point than either of the pure diasteomers and it would be moderately broad.