My new rebuilded denso starter (Heat soaked?)

[Ivan141]

Hows your battery? I had this once with a nearly dead battery, it couldnt supply the huge start current demanded by the starter and would just go click (or f@cking tak as you so eloquantly put it ;-)).
Before going crazy with other solutions, try to borrow a decent battery and try that out.
If the starter actually starts turning before slamming to a halt then you might have an ignition timing problem, but that's relatively rare. That would result in the starting troubles when hot as well, but it's a very different click to the one where the starter wont start turning (louder).