From memory, copper wire has a 0.4%/C coefficient. That means that if the wire has a 100 degC temp rise, it will increase by 40%.
25A in 0.0016 ohms is 1W. If you put 1W into a bare copper wire, it will get a lot hotter then 100 degC temp rise.
So forget about a 10 bit ADC. Most of the bits will be meaningless.
Perhaps a 2 bit ADC will be about all you can manage with the wire.
If you do try it, you have to try a way of conducting the heat away from the wire. Where copper wire can be useful is where you actually want the resistance to increase with temperature. A bit like a PTC thermistor. Even with no added heat in the wire, if the ambient can go from, say, 0 degC to 40degC, that means a change in the resistance of 16%. If you can keep the temperature rise to 10 degC, that means you end up with an accuracy of 20%.
You are much better off buying a current shunt resistor.