It is more complicated. The thicker wire is less resistance, and you need more surface area to equal the old_resistance / old_current. Or you can get more current because it is less resistance.
However, thinner wire gets hotter with less current. YOu can google it or check wikipedia for a fixed current in NiCr and the temp tables. *** However this assumes no air or heat loss from vaping a liquid sputtered onto the coil...
The main thing I've come to decide on is for a given battery, you can optimize what current you want to maximize its life (unless you get LiPo).. Then there is a given resistance that corresponds. People are.. well just stupid using 10W power resistors to generate wasted heat. It makes zero sense.
There is also a limit to how much you can heat up the atty before the solder joints go.
I'm not sure the thickness matters other then bouncing around in your pocket, or blowing compressed air into it. Your toaster works fine. It is possible that red-hot thin NiCr are breaking like a lightbulb filament... but I haven't seen enough post-mortums reports to justify this. I think the NiCr can burn just fine red hot. Now if you are jarring a hot atty, that is another matter..
A lot of atty have regular wire going all the way up to the wrapped coil. Some atty have longer NiCr leads back towards the battery side.