My k75RT is my touring bike, and I've had it in New Mexico and Utah in 120+F without suffering excessively. The main source of heat now is the hot sun beating down on my riding gear and the lack of airflow because of the windshield. I solved the airflow problem by getting a cut down windshield for hot weather riding. I helps a lot, but can't be done with the power shield on the K11LT.
The main thing is to keep the fuel in the tank as cool as possible. There are two approaches that I know of to accomplish that. I built a fuel cooler and put it in the return line to the tank and put it in front of the radiator. It works well enough to keep from frying my thighs and boiling the fuel in the tank. I am not sure if the extruded aluminum cooler I used will fit in the space between the wheel and the radiator on the K11.
Another solution I've seen is to move the pressure regulator from the space behind the radiator to a spot above the fuel rail below the return spigot on the tank. This moves the regulator out of the hot air coming off the radiator and engine block to a cooler spot behind the radiator trim. It's a fairly easy modification that only requires a simple sheet metal bracket to be made and attached to the left side frame down tube. A nice additional touch would be to put a little reflective insulation behind it between it and the radiator along with a few holes in the radiator trim to put a little cool airflow on it.
Another approach is to put an insulated blanket below the tank and seat to reflect the heat rising from the engine. There is information here, just search on "Johnny Blanket". Yes, we can thank our own beloved forum honcho for this invention.
The brick will never be as cool to ride as a boxer, but by adding the Johnny Blanket and keeping the fuel cooler you can make it more comfortable in hot weather.