2001 cadillac deville, overheats without loss of coolant

bad fan. for fuse blow or relay to it dead.
or clogged RAD tubes(inside)
tests are easy ,ask.

at high speed cooling system needs no fan
as you slow it does.
all cars /trucks.
scan the PCM (car) yet< it may tell you why.
fuses ?

Two cooling fans controlled by three relay's . If only one fan is working ,that could be a problem .
Coolant Level Sensor Description
The coolant level sensor monitors the coolant level in the cooling system and indicates if the coolant is low. This sensor is located at the base of the radiator surge tank and is not serviceable.
CHECK COOLANT LEVEL (2)
The IPC receives a discrete input from the engine coolant level switch. The engine coolant level switch is normally closed. When the engine coolant is low, the engine coolant level switch opens. When the IPC receives an open signal from the engine coolant level switch, the IPC displays the message on the DIC.

Relay Driven Dual Cooling Fan Diagnostics There are using a pontiac , by your cadillac is the same .

you have damage in heater cor system you can cancel it by pass two hose gose to cabine temporary to avoid overheat your engine ,then you have to replace heater cor down dashboard

blockage in rad, headgasket or maybe a faulty sensor,you need to get a presher test done on the cooling system first.

This item is located in the resevoir, by the brake master cylinder. The Northstar has a head bolt problem, that allows compression gases to enter the cooling system, and that blows out coolant. Loss of heater, loss of coolant, eventual overheat are common symptoms.

But, top up and see of the issue comes back. If it does, have the cooling system checked for exhaust gases..... Extremely expensive to fix CORRECTLY.

The Dexcoolant is known to evaporate one quart a month if driven 1000 miles or more each month
The reason for its a man made liquid that can not withstand temperatures such as the old style coolant we use to use

A head gasket leak is usually indicated (among other things) by continous overheating of the motor, and subsequent loss of coolant.
It can also be indicated by the presence of engine combustion gas bubbles in the coolant resevoir.
Ensure the coolant system has no external leaks, such as faulty hose/s, radiator etc.

Ensure motor tune or other motor mechanical condition is not the cause of overheating.
I assume the motor is actually running hot.

Check cooling fans are operating ok (as necessary when car warms up):- if not check
1) fuse,
2) relay operation,
3) heat sensor switch.

Check/replace the thermostat,
Check the coolant pressure cap is serviceable & of correct rating,
Ensure cooling system is correctly filled, bleed off any airlocks as necessary when re-filling,
Ensure radiator hose on suction side of waterpump is not collapsing at engine revs above idle (due softening),
If the motor has been severely overheated, the head gasket could be blown - look for combustion gas bubbles in the coolant resevoir.

Check the radiator, hoses, and water pump for leaks. If you don't see any coolant loss, the problem is most likely a faulty thermostat. Hope this helped and best wishes.

Sounds more like an ignition control or coolant flow problem. Or, a/c fan not coming on with a/c.
Getting the water pump question out of the way, the pump either works or not. If it leaks it will cause an overheat due to coolant loss on flat ground or grades...doesn't matter. If the pump bearing or seal is bad it will still pump, it will just be loose and noisy. Coolant flow through the radiator is also essential...I don't think you have a problem there because generally this happens with less maintained higher mile cars.
A bad map sensor can cause your problem because it changes both ignition timing and fuel mixture, either of which can cause very high temps in combustion chambers especially when under a load. Mass air flow sensor can also do this but usually will cause idle problems. If fan is not on with a/c if the remainder of your cooling system may be enough to maintain decent temp control but cannot do this under a load. A/C turned off removes some load and therefore allow you to get up hills. Operating marginally, you can be pushing some coolant out of the system at times without even knowing it.
Now, about your engine: These engines are in my opinion a very poor design to begin with. Even with the best maintenance and low miles, they don't handle temperatures well. at this point, I'd be concerned that after repeated overheats and near overheats, your head gaskets may have started to fail, even though they were not the cause of the problem.Keep that in mind.
Have the items I mentioned tested. If you finally have the problem solved I suggest you change the thermostat as well...Overheating makes them unreliable.

I had the same problem with my 2001 Cadillac Deville, like you I had replaced literally everything thermostat, water pump, radiator, temperature sensor, reservoir and cap, hoses etc....I didnt have any leakage. I was told I had air in my coolant system. After a lot of research and running across the right mechanic I was able to locate the bleeder and remove the air from my lines. No problem since. The bleeder is located on yhe left side of the radiator on the crossover, mines was sideways..Hope this helps someone before they spend money for new head gasket problems..Try this it helped me....