We have an old Weller WTCP2 solder station that has a temperature dial that only goes from 200° F to 450° F. Since rosin core solder is typically used with irons around 700° F, we do not understand the purpose of this solder station and cannot find any information about it on the web. It does melt solder, but does not have enough heat to create a reliable solder joint when trying to join wire to a contact.
While those numbers certainly sound like they should be in Celsius, I'll take your word that it at least says Fahrenheit. That would still be a usable temperature range, but just for very small and highly sensitive work.
I've definitely dropped my iron into the low-mid 400's for some micro SMD and 40+AWG wiring tasks. You'd also need 0.015" wire or solder paste, if not just reflowing a joint. It's rare, but not completely unheard of.
No idea why it would have a range below the melting point of solder though (361F for 63/37). If that's not just a typo on the label, it would be a nearly useless iron 99% of the time.
In regards to your claim of 700F being the right setting for most solder, I do almost all of my work between 550F-650F with 0.031" 63/37 wire. If you regularly have to get anywhere near 700, you might want to invest in some better flux and solder and/or double check your technique.