There’s a lot of information in this thread, and some of it is correct. But as a long-time metal caster, there are some errors that strike me.
First off, the idea that the positive model will be cleanly and instantly replaced by hot metal is wrong, if you’re talking about a model made from PLA, or even wax, and encapsulated in a plaster-based or ceramic shell mold. There is a process that works that way, but only with models made from polystyrene-based foam, and only when it’s encased in loosely packed sand.
Models made from other combustible materials need to be fired in a kiln (not baked in a home oven) to burn away the model before introducing the metal to the mold. The model must be completely gone, without a trace of carbon or any ash left in the mold. Failure to do this will result in surface defects or incomplete castings, and can lead to dangerous explosions, especially if the mold is gypsum plaster based, which retains chemically bound water up to 1000 degrees F. Wax models are usually fired to 1250 degrees or so, but PLA, which doesn’t flow out of the mold when heated, like wax does, needs more heat and time in the kiln; about 1450F is typically recommended. (Introducing extra air into the kiln during burnout helps combust the residual ash.) This is where conventional plaster-based jewelry investment - a mixture of gypsum plaster and silica flour - reaches its temperature limit, so other formulations can work better. There are investments made for platinum which can tolerate more heat, and also some made especially for plastic burnout. Ceramic shell is another alternative, but it’s a lot more hassle to set up and much slower, since successive layers need to be applied and dried to build up a sufficiently thick mold.