Not if it were functioning correctly. I would change the thermostat on the chance its sticking closed, but if its really that hot, it shouldn't be closing at all. I'd replace the thermostat before I would replace the water pump.

Two different gauges reading the same temp is pretty likely accurate. I suppose you could always check it with another gauge, but what do you do if that one reads differently? Which ones do you believe? Maybe you should add an oil temp gauge, that would let you know if the motor was really hot or not.

240 is hot enough to damage a motor. Gene