... and then will start again once it's cooled back down. This is a typical symptom of a failing Hall Effect sensor. (a.k.a. HES) The Hall Effect sensor sends timing signals to the fuel system so the fuel system knows when to fire the spark plugs, etc... The HES is located under the roughly 4" square "T" shaped cover on the front top right of the engine.
There's a couple of ways to crudely troubleshoot to see if the HES is the culprit.
1- Cool it down. When the bike warms up and quits splash some cold water on the HES cover to see if that cools the HES down and allows you to restart the bike.
2 - Heat it up. This is probably most effective if done with the HES cover removed but there's a good chance that you'll need to replace the cork gasket for that cover. Start the bike up and point a heat gun at the HES to see if you can induce it to kill the engine.
Replacing the Hall Effect SensorReplacing the HES is straightforward and easy to do:
It's connector is located under the left front of the gas tank so you'll need to pull the tank back to access it.
You'll also probably need to remove the right fairing lower to cut the zip-tie that holds the wiring to the frame near the lower right corner of the radiator.
Once you've removed it's cover plate remove the two small Allen bolts that hold it in place. (Blue circles in the picture below.) Be careful not to lose the two small indented special washers that hold it in place. This will make more sense when you see what they look like.
Install the new one with the special washers determining it's exact location. In theory you should then check the timing with a timing light but that's a PITA with the forks and front wheel in the way. What I've found is that carefully lining up the notch on the HES plate with the notch where it mounts will set the timing correctly so a timing light really isn't necessary.
K75 HES part number: 12111459049
K100, K1 and K1100 HES part number: 12111459033
