All it take to overheat the wiring and connections is some extra resistance and a high current draw. The connection or wire with the higher than stock resistance creates heat, which creates more resistance, on and on, it's a vicious circle. What happens then is that the wire or connection finally fails, sometimes in fire or if you are lucky, it just quits working.
A voltmeter is handy if you are familiar with how to use it to find bad connections. Measure the voltage drop across a connection while trying to start the car: more than .1 volts across a connection indicates a problem. The voltage drop tests need to be done while maximum load is on the circuit under test. It's the current flowing through a connection or wire that causes the voltage drop.
See http://assets.fluke.com/appnotes/automotive/beatbook.pdf for help for help troubleshooting voltage drops across connections and components. .
Voltage drops should not exceed the following:
200 mV Wire or cable
300 mV Switch or solenoid
100 mV Ground
0.0V Connections
A voltage drop lower that spec is always acceptable.