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For my DMX project (schematics is not important), I soldered this temperature fuse which has just two leads (see picture below).

The fuse doesn't work (meaning it does not conduct electricity) ... which of course is logical since my soldering station has a minimum temperature of 200 °C (392 °F) (although I soldered it with 350 °C (662 °F), forgetting about this).

But how should I solder this component?

I think those thermal fuses are normally connected using crimp terminals, rather than by soldering.

Even with the heatsinks the other answers mention, it would be much too easy to damage the device while soldering wires to it.

This was a problem with transistors in the early days and standard advice was to use a pliers as a heat shunt close to the body of the component.

Figure 1. Protecting a capacitor from overheating when using a big ignorant soldering gun. Image source: Mother Earth News.

Oddly enough, the image above was the only one I could find in an image search. The technique may be getting lost. A long nosed pliers with a rubber band on the handles may suffice and the rubber band will hold it in place freeing up one hand.

You can use a heat shunt - really just a pair of pliers on the lead, and keep the soldered joint as far away from the body as practical, but ideally use crimp joints, soldering these things is always tricky.

Soldering stations which can be set to much lower temperatures than 200°C are not unheard of (and wide temperature range somewhat correlates with quality). If you had one of these, you could use low-temperature solder like chipquik.

For a one-off job and considering your space constraints, you could simply solder copper wires where the fuse needs to be, then twist these wires with fuse terminals, which is not as good as crimping, but does get the job done in practice. Twisted parts can then be trimmed to save space (3-4 twists is enough) and heat-shrink could be put on if insulation is required.

Another idea is to bend the fuse terminal in a snake-like pattern to save space, and then solder the ends of therminals, while cooling down the therminals entering the device (e.g. by holding them with a wet cloth).

As was mentioned in other answers, crimp termination would be best. Followed by a pin or screw terminal.

Since you seem stuck with the design and don't have space for a pair of heat sink pliers, there is one other option if you must solder it.

Wrap the component as much as possible with a lightly damp kimwipe or other low lint cloth. Make sure it's distilled water and allow it to dry completely before energizing the circuit.

Not ideal, but I've used it successfully in the past for tight spaces and heat sensitive parts. You may even be able to chill the water provided your fuse can handle cold without damage.

My suggestion, given your lack of space is to attach with conductive silver epoxy. This will give you a fairly robust conductive connection with no application of heat.

Do as everyone else does. Wrap the therm with a ziplock bag of ice. Then solder away. A wet wrag placed in a fridge is the preferred method.