Hi,
If you want to make a current shunt it doesnt matter what any other meter had read in the past, you'll be reading Amperes.
Copper isnt such a great metal for a shunt, brass is a little easier to use because it has about four times the resistance. You can get brass strips at the hobby shop or hardware store. You can calculate the resistance of a brass strip by assuming a resistance 4 times that of copper.
The temperature will affect the shunt, but how much it bothers your reading depends on how much accuracy you really need, and you probably dont need super perfect accuracy. If you want more accuracy, you'd have to mount a sensor next to the shunt in thermal contact with the shunt metal but not electrically in contact. This way you can measure the resistance of the sensor and determine how to adjust the reading.
But another issue that is quite important is the input offset of the op amp being used. You'll want to use an op amp made for very low input offset and low drift like a chopper stabilized op amp. That will give you the best results for measuring a DC current using a shunt. You can adjust the gain to match the shunt resistance.
A brass strip 0.0167 inches thick and 0.25 inches wide and about 1.5 inches long (a flat strip) has a voltage drop of 1mv per amp (0.001 ohms resistance) at 20 degrees C. The temperature coefficient of some brass is one half of that of copper, but unfortunately for some other brass it can be as high as twice that of copper. But using a sensor for feedback it doesnt matter as much.
A piece of AWG #12 copper wire about 7.6 inches long has resistance of close to 0.001 Ohms, and as the temperature rises by 10 degrees C the resistance increases by about 4 percent, so it goes from about 0.00100 ohms to about 0.00104 ohms. That would produce an error of 4 percent if calibrated at 20 degrees C room temperature. If that's too much then a sensor would have to be used to estimate the shunt temperature. A sensor might be able to be made from a much thinner piece of copper wire wound around the shunt wire to detect the temperature of the main wire. A short calibration procedure would make it all more accurate still.
A four wire connection is normally used here. That's where the (say) 7.6 inch piece of copper wire is extended to maybe 12 inches, and the current is run through that, but the connections for the sense wires are made right on the wire itself somewhere in from the ends such that the sense wire connections are 7.6 inches apart even though the wire is much longer. The current is fed into the ends, but the sense voltage is taken from anywhere between those ends but not directly on either end. The current feed wires have to be heavier gauge (like 12 gauge or more) but the sense wires can be #22 for example.