Here is a diagnostic table from the service manual:

Document ID# 296409
1998 Oldsmobile Intrigue
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Engine Overheating

Step
Action
Value(s)
Yes
No

DEFINITION: The engine temperature lamp comes on and stays on, the
temperature gauge shows hot or coolant overflows from the coolant recovery
reservoir onto the ground while the engine is running.

1
Check for a loss of coolant.

Has there been a loss of coolant?
--
Go to Step 2
Go to Step 3

2
Refer to Loss of Coolant .

Does the engine still overheat?
--
Go to Step 3
System OK

3
Check for a loss of system pressure.

J 24460-01.
Refer to Cooling System Leak Testing .
Has there been a loss of system pressure?
--
Go to Step 4
Go to Step 5

4
Correct the system pressure.

Does the engine still overheat?
--
Go to Step 5
System OK

5
Check for low coolant protection.
Ensure that the solution is at the specified temperature.
Is there low coolant protection?
-37°C (-34°F)
Go to Step 6
Go to Step 7

6
Correct as necessary.

Does the engine still overheat?
--
Go to Step 7
System OK

7
Check the drive belt tension. Refer to Drive Belt Diagnosis in Engine
Mechanical-3.8L.
Check the tensioner.
Is the tensioner working properly and the tension correct?
--
Go to Step 9
Go to Step 8

8
Replace the tensioner as necessary.

Refer to Drive Belt Tensioner Replacement in Engine Mechanical-3.8L.

Does the engine still overheat?
--
Go to Step 9
System OK

9
Check to see if the timing is retarded by a malfunctioning Powertrain
Control Module (PCM).

Is the timing retarded by a malfunctioning PCM?
--
Go to Step 10
Go to Step 11

10
Correct as necessary. Refer to Powertrain Control Module Diagnosis in
Engine Controls-3.8L.

Does the engine still overheat?
--
Go to Step 11
System OK

11
Check to see if any of the radiator fins are obstructed.

Are any of radiator fins obstructed?
--
Go to Step 12
Go to Step 13

12
Remove or relocate any add-on parts that block air to the radiator.
Remove any debris from the radiator fins.
Does the engine still overheat?
--
Go to Step 13
System OK

13
Check to see if any of the cooling system passages are blocked by rust or
scale.

Are any of the cooling system passages blocked by rust or scale?
--
Go to Step 14
Go to Step 15

14
Drain the cooling system. Refer to Draining and Filling Cooling System .
Flush the cooling system. Refer to Flushing .
Repair as necessary.

Does the engine still overheat?
--
Go to Step 15
System OK

15
Check for a pinched or kinked coolant recovery reservoir hose.

Is the reservoir hose pinched or kinked?
--
Go to Step 16
Go to Step 17

16
Replace or reroute the hose as necessary. Refer to Coolant Recovery
Reservoir Replacement .

Does the engine still overheat?
--
Go to Step 17
System OK

17
Check for an inoperative cooling fan. Refer to Electric Cooling Fan
Diagnosis in Engine Controls-3.8L.

Are there any inoperative cooling fans?
--
Go to Step 18
Go to Step 19

18
Repair or replace the electric cooling fans as necessary. Refer to Cooling
Fan Motor Replacement - Electric .

Does the engine still overheat?
--
Go to Step 19
System OK

19
Check for a loose, damaged, and/or missing deflector.

Are there any loose, damaged, or missing deflectors?
--
Go to Step 20
Go to Step 21

20
Replace the deflectors.

Does the engine still overheat?
--
Go to Step 21
System OK

21
Check to see if the thermostat is stuck in the closed position. Is the
thermostat stuck in the closed position?
--
Go to Step 22
Go to Step 23

22
Replace the thermostat. Refer to Thermostat Replacement .

Does the engine still overheat?
--
Go to Step 23
System OK

23
Check for a faulty coolant pump.

Is the coolant pump faulty?
--
Go to Step 24
Go to Step 25

24
Replace the water pump. Refer to Water Pump Replacement .

Does the engine still overheat?
--
Go to Step 25
System OK

25
Check for an incorrect radiator.

Is the radiator correct?
--
Go to Step 26
--

26
Install the correct radiator. Refer to Radiator Replacement .

Does the engine still overheat?
--
--
System OK