Wire has resistance. Current flowing in that wire produces heat in the form of I**2 * R losses. This energy being dissipated in the WIRE (Wicked Infitesimal Resistance Element) raises the wire's temperature. This temperature rise affects the wire's insulation. Insulation can only take a certain temperature before it melts, or carburizes. The best insulation is Teflon, it is good up to 200 degrees C. It is expensive however.
The following graphs from MIL-W-5088L has everything you need to know to size your wire system: Wire Rating Tables from MIL-W-5088L
Fusing current is sort of neat. This is the current it takes to "blow" the wire up. I sometimes use short jumpers of #30 on a PCB to get a poor man's 10 amp catastrophic event fuse in a circuit that usually draws no more than 1 amp or so. Fusing Currents of Wire
Here is a short graph that will help you size your PCB traces for ampacity: PCB Ampacity for Trace Dimensions
Now here is a paper on the meaning of temperature rating for motor winding wire by Essex: Magnet Wire Temperature Rating and What it Means
For info: Silver or tin plating is used to protect bare copper from heat and chemical accelerated oxidation. Silver is used instead of tin for high temperature applications. In aerospace we use crimp connections as they are more reliable than soldered, when vibration is considered. For high temperatures silver coated copper makes a "nice," stable, low ohm crimp connection.
--bigMoose who doesn't know what he is doing with Wiki! 08:05, 29 August 2011 (MDT)