With respect, I think you may be chasing your tail. As deQuincey suggested, why not determine that your engine is actually overheating before attempting to fix something that is not broken. Who can vouch for the reliability/accuracy your temperature gauge? I once looked at an E3 for parts. The engine had blown a head gasket. The owner said he could not understand how it could happen "since the gauge never moved out of the blue."
Your gauge or the sender may be extremely accurate as-is, or it may be way off due to any number of possibilities, including poor grounds, loose or poor wiring, etc. Consider obtaining a reliable aftermarket thermometer or a point-and-shoot thermometer and take some readings. Even without a secondary gauge, does turning on the heater have any effect on the temp gauge? Hint: even a wee bit 'o corrosion on that coolant temperature sender and/or the attached wiring can render it unreliable and make some gauges mimic a wiper blade.
Not a slight against your prior mechanic, but even excellent work performed thirteen years ago, does not guarantee perfection in perpetuity. Some metal corrodes, rubber deteriorates, silt can compress into immovable sludge creating unforeseen arterial blockage and ossification. Unless you are using a special waterless-coolant, e.g., "Evans waterless coolant", flushing the cooling system and replacing the coolant is standard maintenance whether the car is stored or operated, even occasionally.
What was wrong with the waterpump that required its replacement? Are you using the upgraded fan and viscous fan clutch?
What was wrong with the thermostat? Did you test the thermostat, even the new one, to determine that it functions properly? What was the temperature rating for the new t'stat?
What type of coolant did you remove and/or install? Not certain, but some types are evidently disfavored due to an alleged proclivity to congeal under the wrong circumstances.
http://www.sancarlosradiator.com/dex-cool.htm
I generally would not go to this length. But if I suspected a cooling issue - and had a radiator sitting for a long time - I would seriously consider removing the radiator from the car and (carefully) flushing it from all angles with water. IF the radiator had sludge at the bottom of the tank, a typical flushing,
in situ, might be ineffective and blockage or potential blockage might remain despite a clear running stream.