kz400 over heating?

After riding around for 30-40 minutes or so, my bike will start to smoke (blue-ish) and eventually no longer idle. Usually it'll die and then I'll need to wait a minute or two before I can either kick it over or use the electric start.
I looked at the plugs and they're black on the tips (running rich?). So is this a matter or air / fuel mixture that needs adjustment at the air / fuel mixture screw? Oil level? (My oil level window on the right side of the engine is jacked so I cannot really tell how much is in there...)

Any experience with this? What can I do to keep this engine cool?
R

That thing is air cooled, right?

If so, all you've got for cooling is the fins on the engine and the oil. Are the fins clean and clear of grease and debris? Have you recently painted the fins? I have heard from a few people that engine paint can cause issues because it likes to hold the heat. Aluminum has really good heat transfer properties. It heats up quickly, heat transfers through it quickly, and it cools down relatively fast, which makes the air cooled system work well on it.

I would check that oil level before riding it. If the glass is jacked, find another way to check it. You can stick a piece of wire into the fill hole, and use that as a dipstick. Might be your best bet. I don't see fuel-air mixture problems causing it to overheat. Also, if you do have sufficient oil in there, it could be that the oil is not moving properly. When is the last time you changed it? Maybe some passages are clogged?

The engine was painted by the original owner, however I managed to get most of the remaining paint off of it. I bought the bike a little over a month ago and changed the oil at that time, but not the filter. Now that I think of it, the bike was last titled in '86 so that filter may be THAT old. Could that be the problem? Maybe a filter change?

should be a bypass for the filter so it ca continue circulating even if the filter is clogged. Change the filter, check your oil level, and try to figure it out. Grab a few beers, and sit and think on it. There isn't much to those bikes. It's something simple.

Make sure you determine that the oil is flowing, though. It's the only defense against heat apart from air flowing past the fins.

How can I test that the oil is a flowin'? I will gladly think about it with beer in the meantime

Something else you may want to consider: Sometimes an ignition coil will have an open in its windings. When it is cold the winding wires will touch. As it heats up the wires will pull apart. Once it pulls apart far enough you lose spark. While they are pulling apart the spark gets progressively weaker. That means the fuel mixture will not burn completely leading to fouled plugs and blue smoke. You will have to check the plugs for fire when the bike is hot and quits. Carry an extra plug to use for testing so you don't burn the crap out of yourself pulling the plugs that are currently in it out. If you are losing spark when hot some shops still have coil testers and can verify that the coil is your problem since there are other reasons you could lose spark when hot.