I have Weller WD1.
It has primary fuse and thermal fuse in transformer.
Problem is that 110V version specifies fuse of 1 A. 1A fuse will not blow if you connect 110V station into 240V in a time to save transformer.
Transformer might or might not overheat into short circuit. Some of them will just keep on smoldering. If primary wire is thin enough, it might even fail open.
Transformer wire coating is temperature resistant and flame retardant. If you heat it enough, it might char and become conductive, but not short, not immediately...
Current will rise slowly, until it finally either shorts, or breaks open.
If device catches fire it is usually case or something else made of non fire retardant plastic.
If exists thermal fuse will trip and kill off transformer. Thermal fuse is permanent disable, because if it trips, it is considered that temperature was so high that insulation of transformer was compromised, and should not be used anymore even if it seems to work.
Transformer can be designed to fail open.
Primary fuse is there mainly if short circuit does happen, and serves only to avoid your external fuse trip on a power distribution, so it doesn't shut off other devices.