John Deere tractors from the 1950s and earlier did not have water pumps. They relied on convection to move the water. The problem was the water passages had to be much larger. The upper radiator hose eventually reached a diameter of somewhere around 4 inches(!) before John Deere threw in the towel and added a water pump.
Another proposal was to run on methanol. Methanol burns at a much lower temperature, so an engine specially designed for methanol would not need a typical water cooling setup. Air cooling is sufficient. Of course, there are old Beetles, with their air cooled engines in the rear. I recall vagulely that it worked, but shortened the engine's life.