Interesting, keep us informed. If the engine is actually heating up it could be lots of different things, especially if the radiator and engine passages are clear.
I ran across an 'overheating' problem (not seriously high, just moved higher) with one car, not a Kaiser, because the thermostat was missing. There was enough heat transfer through the radiator at lower engine speeds but at higher speeds there wasn't enough restriction to make for an efficient heat transfer through the radiator as the pump moved the water too fast. (The gauge moved immediately when I turned on the heater fan, because that actually removed some of the heat from the system)
Other than that, I would think the problem is some sort of 'lean burn' situation, were there is not enough fuel/not enough spark? being delivered in relation to load and ignition advance. Could there be a partial plug in the fuel flow, so that enough gas is delivered at lower speeds, but it starts starving as it runs faster, and you overshoot the advance?