Some times a ballast does not like to see the on and off of the ignition during crank. You can add a capacitor to hold the voltage steady during crank. Your connectors should not be getting hot. A loose connection will cause the plug to heat up. Another cause could be that you are pulling to many amps than the connector allows. You can add a relay if one was not installed to get power directly from the battery and the headlight would be the turn on signal to the relay.