Which wire are you talking about getting hot? The one from the positive battery post, the negative battery post, or the smaller one that goes to the starter solenoid?
Wires generally get hot from either being shorted out or from there being too much electricity/amps flowing through them.
There is a clutch switch at the clutch pedal, that won't allow it to start (what it does is actually not allow voltage to reach the starter solenoid) without the clutch being pushed in, therefore pushing the clutch switch in. But since one of the wires at the starter is getting really hot, you are getting voltage to the starter, so I'd say the clutch switch isn't the issue.
I guess you could pull the starter off and bench test it. Negative wire to starter case, positive wire to starter motor post...it should spin up.
I guess you did say earlier that the starter will click (well, it is probably actually the starter solenoid you are hearing click). So you are getting voltage to the starter, but probably not enough voltage to actually operate the solenoid. You replaced the starter, so you know it isn't a starter issue. The only thing left is a clicky starter issue...which has already been covered.