One issue here is that those cheap necklaces tend to be “pot-metal”. I think that’s usually some version of pewter, probably a lead-free pewter. It looks like it needs a new loop attached on one side? I would be inclined to use something like JBWeld to glue a new loop on. Heating pot metal is dubious at best. Plus, cheap clear things are probably glass. Those are fairly small, so they might not shatter from thermal shock if you were applying heat to the metal.
Also, as I think about pot metal, it might be a zinc alloy of some type. Zinc is very problematic if you heat it. It creates a vapor that is a very bad compound of zinc.