Water pump failure will not create intermittent issues. Usually the first sign of a failing water pump is coolant leakage from the weep hole. I don't think the problem is a thermostat, as they typically fail in the open position and cause the engine to run cooler than normal, not hotter. Could be a defective temperature sensor, contamination on the cooling surface of the radiator, or coolant circulation issues.
I would start by thoroughly cleaning the radiator (use Simple Green), a complete flush of the cooling system, and fresh coolant. This might fix your problem, but even if they don't you have not wasted your money since these are good basic maintenance items.
2001 Bonneville SSEi (retired at 365,000 Kms.)
2014 Jeep Grand Cherokee Overland (yes, I know its not a GM)