What are the safest temperatures to heat different filaments to?
Polycarbonate is heat-resistant up to ~120C. Above this temperature it will gradually become flexible and may irreversibly bend. It will not generate any toxic fumes all the way up to ignition temperature (630C), because it's fumes are not considered harmful. Note though, that with your temperature limit you may not be able to print with polycarbonate, or only do so at a very low speed.
According to the sheets of commercially available printable plastics, PC has the highest printing temperature and heat resistance among them, seconded by nylon. This refers to the FDM printers only. SLS printers may be able to use other materials, even metals like aluminum or titanium, so if you really wish to get temperature-resistant prints, you may look for workshops that have SLS printers and ask them.