Cadillac Repair: 99 Cadillac Seville SLS overheating, cadillac seville, neutral temperature

Question
Hi, I'm joining the "Northstar overheating crowd".
Replaced the thermostat, still overheating. But! I have a diagnostic hint: when at low RPM (idling in traffic or going 65 on a level highway or even rolling in cool air down a long hill at 75 mph with engine idling on neutral) it overheats into the red zone; but if I run it for a minute at 3500-4500 RPM regardless of the load (accelerating uphill or just revving on neutral) - temperature goes back to normal within 20-30 seconds, then at lower RPM it creeps up again. Looks like restricted coolant flow or worn water pump to me: at high RPM at least some coolant recirculates between the engine and the radiator. What should i replace first? Should I still check for blown gasket? Engine runs smooth and there is no lack of power.
Thank you in advance for your time and expertise.

Answer
I would try and first replace the water pump which requires a special tool on the 4.6L engine.

If you are mechanicaly inclined or know of someone who is, You will need simple electrical schematics, Test procedures and picture locations of the components within the system that is causing you problems of which can't be done on this website which only allows one picture. I do not have a website so you will have to e-mail: onlineautohelp@msn.com in order to obtain the information.