[cleszkie]

Based on the color of the smoke, my money is on unburnt fuel, not oil, exiting your exhaust. Water makes white smoke, oil makes blue smoke, and fuel makes gray/black smoke. That would explain why the truck runs when cold and not when hot. When cold, the excess fuel is acting like a choke, and the engine can deal with that. When it gets hot, and the excess fuel is still acting like a choke, the motor dies.

Maybe a stuck needle valve is causing float bowl to flood. Maybe a leaking accelerator pump. Just something to consider.