2008 International 4300 - DT466 - No Start When Hot

I have an old DT466 that runs great all day long, but if I shut it off to get lunch, it won't restart until the engine cools down for an hour. It cranks fast enough, but it just won't 'fire'. If I spray a tiny bit of starting fluid, it kicks over, but I know that's bad for it. Once it's running, it has plenty of power and doesn't smoke. I suspect something in the high-pressure oil system is leaking when the oil gets thin and hot.