Tests before you open things up:
Heat your mechanical fan clutch with a hair dryer, and see if the resistance to turning the fan increases (it should.) If it does not, replace the fan clutch. Typical life seems to be four years or so - when you put the new one in, take a Sharpie pen and write the date on it.
What year? You can usually test the thermal fan switch with a hair dryer as well, if you're patient. Or, let the engine idle and monitor coolant temperature with a non-contact IR thermometer near the TFS (location varies by year. 1987-1990 has it in the driver's side radiator tank, 1991-up has it in the thermostat housing. The ECU triggers the fan relay on 1991-up models, so it can be a bit more involved.) 1987-1990 is a simple thermal switch - it should "close" (zero resistance) up somewhere around 215*F, as I recall. 1991-up units are "thermistors" and will follow a predictable curve as temperature increases. I think I've posted it here before.
You have a pressure leak somewhere, which allows the coolant to boil at a lower temperature (each 1# of pressure in the system increases the boiling point by 3*F.) The 242ci six likes to run ~210*F, water boils at 212*F. Not much room there (antifreeze depresses the freezing point of coolant, but doesn't do much for the boiling point. Tangent - has it been changed in the last two years?)
You may have an "air pocket" behind the thermostat - they can accumulate with time and gradual overheating. If/when you put the new one in, drill two 1/16" or so holes in the flange where they won't be covered by gasket. Install with one hole at 12:00 and the other at 6:00 - that takes care of that.
Your electric fan motor may have failed - easy test. Unplug it, grab your DMM, and check resistance between the two pins. I don't recall what it should be, but it should not be either "zero" (indicating a short) or "infinite" (indicating an open.) Either result indicates necessary replacement.
The electric fan relay may have failed - you'll need a 9V battery and a pair of clip leads for this one. Connect your meter to pin 30 and pin 87 on the relay, you should see infinite resistance (open circuit.) Leave the DMM connected, and connect the battery to pins 85 and 86 on the relay (doesn't matter which is which.) Your DMM should show zero, or close to it. Replace if not. Location of E-fan relay varies year to year.
Grab your non-contact thermometer, let the engine idle, and take readings across the radiator core as it heats up. There should be a definite downward gradient as you move from the passenger side to the driver's side, and it should also decrease slightly as you move downward. If you note any spots that don't heat up or don't cool down, you have a clogged core - and should get it seen to (if a flush doesn't correct it, take it to a radiator shop to have it "rodded out" or replace it outright.)