Well, it could actually be two different things, not just overheating.
But...it IS overheating so you need to address that issue first and worry about the black stuff afterwards.
The pee stream should never get so hot that you can't hold your hand under it comfortably while the engine runs.
But don't hold your hand in the stream and shut the engine off. When the engine stops and the pump stops pushing water, the temperature spikes as the water in the block drains for a few seconds and that can scald your skin.
I think that your thermostat may be stuck completely closed. If it is, the engine will begin overheating fairly quickly.
If you've never replaced the thermostat, you should consider doing that.
However, I have also seen waterpumps that had damaged impeller vanes produce a decent pee stream but not pump enough water to keep the engine cool. Again, if you've never replaced the pump, you may want to do that too.
Good luck.