I don't know of a method that doesn't require knowing, or at least estimating, the temperature of the wire.
The way I estimated temperature for the quick test with this NiFe was to heat it to glowing. I then estimated, based on what we discussed the other day, that glowing had to be at least 600°C and because it was orange, was more like 700-800°C.
I then watched the live ohms display on the mod while VW firing, making note of the starting ohms and maximum ohms under heating.
I put the figures into this
TCR calculator, filling in all fields except TCR which it then calculated for me.
It's crude, because I can't be sure of the max temp. But assuming bright glow = 700°C at least gives you a best case TCR (because it probably heated more than that.)
The proper testing I will do with my thermocouple, and potentially a camera to record the temperature alongside the resistance - unless I can just eyeball that well enough.
The DNA 200' could well make it easier - easily showing/recording the maximum resistance, which can be compared against the separate thermocouple log showing maximum temperature. Maximum temp and maximum resistance are surely from the same moment, so put those two figures into the TCR calc to get the accurate TCR at that temperature.
Of course that gives the TCR @ 700°C or whatever it heats to unrestricted. We really care about it only up to 250-300°C.
So once one has a rough TCR, switch to TC mode using the rough TCR figure, thermocouple measure the wire with that rough TCR, check if the wire temperature matches the configured temperature on the mod. Adjust the TCR until it does.
The latter is what I did with eg Titanium, where I already knew a rough TCR which I was only validating - 0.0035 in that case, which turned out to be exactly right.
But you might be limited in what you can do without actual temp measuring. But the "glowing hot" test should at least give you a rough idea, whether it's 0.001 or 0.005 or whatever.
EDIT: sorry I'm sick and not thinking straight. Obviously with the thermocouple, one can just record the resistance when it reaches 250°C. As long as one can see what the resistance was at the moment it hit 250°C, one already has the TCR to 250°C
So either timestamped logs from both escribe and thermocouple, or failing that escribe window next to thermocouple log window, and screen capturing software, so one can re-watch the video and see what the resistance was when it hit the target temp.
One could also heat it gently, say 10W, with airflow, to minimise the heating so it doesn't overshoot
Shouldn't be a need to re-tune the TCR after that.