Adding two 1 eV photons in a two-photon upconverter does not give you a single 2 eV photon. Some of the energy of the upconverted photons is lost as heat, so thermodynamically it's okay.
Yes, you are right. Each of these nanoparticles should also radiate heat radiation or heat the environment near it in other way, but it is not clear from the citation.
