No, my friend, I need the interior part with the number 53312699, and the part number 58736795 seems to be the turbine.
Oops, sorry
The 5 33 126 99 seems to be called "Hot air pencil HAP 2" running at nominal 230 V with up to 700 W power.
(Perhaps fire up an email to repair-center (the address is just under the personnel pics
here), asking if one can buy a replacement, considering the product line is discontinued?)
I didn't find anyone selling these online, but it is quite possible Weller or some of its distributors have replacement hand pieces still in stock; after all, this is professional soldering equipment.
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Let's do some math.
First, we know the voltage is 230 V (RMS) and power 700 W. This means the total resistance of the heating unit is 230²/700 [V²/W] ≃ 75 ohm.
This is actually in 18 sections (with a little bit of wire in between, for 4.3 ohms per section),
but a single length of wire. You cannot really join two pieces together: solder will melt, and crimped connections won't hold due to the thermal expansion and contraction.
0.4mm/26AWG nichrome 80 wire has a resistance of 8.0 to 8.9 ohm/m, let's say 8.4 ohm/m. Thus, the entire heating coil will need between 8.4 m and 9.4 m of wire.
If the outer diameter of the coil/helix is 2mm, the inner diameter is 1.2mm, and centerline diameter 1.6mm. Each turn is therefore about 5.0mm, and the entire coil will have about 1800 turns: 100 turns per section. When closely packed, 100 turns of 0.4mm wire is 40mm.
However, the actual power as calculated above may be higher, if the control unit limits to less than 100% duty cycle (in the triac chopping the mains voltage). If the per section resistance is 3.5 ohms, the total 100% duty cycle power would be 840 W (20% more), and whole-coil resistance 63 ohm; about 7.5m of 0.4mm/26AWG nichrome 80 wire.
If the outer diameter of the coil/helix is 2mm, there would be about 1500 turns, or about 80 turns per section (with about a turn in between sections as a straight wire). This sounds more plausible than the above, since the coil is no longer tightly packed.
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I personally would cobble together a rig to wind the entire coil in one long section, then measure (resistance) where the 17 straight sections are.
The entire coil will in all cases be at most 18×40mm = 720mm long. I'd bolt two rod ends at about 80cm from each other through some plank or rod, with ring bolts through the bearing hole, core wire carefully attached to the rings, and tension the 1.2mm core wire between the two using nuts on the ring bolts. I'd use two nuts per ring bolt, jammed. The setup can be rotated from either end using e.g. a cordless drill, so it is a good idea to use longish ring bolts. I'm right-handed, so I'd keep my left hand on the trigger, and with my right hand
carefully tension and feed the nichrome wire onto the core wire. The initial 10-20 turns may not work out too well, so this would be the trimmed end.
Next, I'd pull the coil off the core, and stretch it a tiny bit: just enough to separate the coils, making it a helix (turns not touching each other).
Then, I'd measure the resistance of the first coil section (3.5 ohms using your DMM), then unwind about half a turn for the next section, and push the rest of the coil through the next section hole. Each following section I'd measure the resistance from the previous straight part (the same 3.5 ohms using your DMM), then unwind the half-turn or so needed for the intersection part. If all goes well, you end up with a section of unneeded helix, which I'd just cut off.
You could also count the turns, but I would probably mess up the count.
I am only a hobbyist, so there are no guarantees this will work, though.