Never measured the actual amperage in the tool, but yes it is 'considerable'. Think of your typical soldering 'gun' with a tip connected across the secondary of a significant step-down transformer. Remove the tip and put some large leads from the gun output to the forceps/pliers and you have the idea.
Now replace the gun with a small portable welder. Don't actually draw an arc, but that's the kind of current we're talking, perhaps 50 amps or so through the twisted joint of two #10 wires. Hot enough to solder in a few seconds. But yes, the 'jaws' of the tool get hot too, so it may be a lot of heat is in the small contact surface between tool's jaws and the work.
Well, that's your perogative. But the individual coils within most large motors (up to say about 100 hp) are connected this way. Been done like this for years. Process is a lineman type of twisted splice, solder, insulate, tie down, go on to next connection. The 'tie down' is important to prevent mechanical stress/vibration.
Not that I'm advocating tinning stranded wire under wire-nuts. It's my understanding that the soft solder alloy will 'creep' with time and loosen. When all else fails, RTFM, or in this case, "install in accordance with the manufacturer's directions".
daestrom