slightly OT / starter problem

The starter on the wife's car works fine when the car is cold, but after it has been driven for half an hour or so, it will not crank. The only thing I hear is one click, nothing else. I wait for half an hour and then it starts no problem.
Battery was testet and is ok.
I suspect it is the starter solenoid not operating when hot. Anybody have any more input? Opinions appreciated.
Heres the OT part: car is a '97 Saturn SL2

 

yeah, more than likely needs a starter.That's a good indication that it's drawing too many amps when its hot to turn it over