Radiator fans staying on all the time?

I have a 2007 ford mustang gt. My car does not over heat, but when i turn on the car and it reaches 198F, the cooling fan starts and stays on all the time and it stops only if i turn the key off. It sounds very loud. I changed the coolant myself and the next day it was doing that. I notice that the upper radiator hose is very hot, while the lower radiator hose is cold and not hard. Could it be the thermostat?

I don't know

It can't hurt to have the vehicle checked out. What you describe is more likely to be caused by something you added with the coolant blocking a line than by the thermostat.

One fan run any time the air conditioner is on to pull air over the condenser. 198 is fine, your car probably has a 195 degree thermostat in it.

Turn the A/C off and the fan will go off.

Nothing wrong with your vehicle except maybe for the fan motor bearings that might be failing. A stuck closed thermostat will over heat the engine. A stuck open thermostat would result in an engine that takes a long time to reach operating temperature.

Run the motor for 15 minutes with the radiator cap off. Watch for air bubbles purging out of the radiator neck. If you don't have pressure in the radiator hoses you either have an air bubble or the radiator cap is bad.
The radiator/condenser fans will run all the time if the AC is on or if you have the air flow set to the floor/windshield position as that turns on the AC automatically on many vehicles.

If the fan is running then it should stay running even when you turn the key off. (for another minute or 2) That is normal., as the cooling fan runs independently from the ignition switch.
. So something is not right with your car. Let a mechanic see it and fix it. Otherwise you will be into problems at some future point. Tell the mechanic EVERYTHING YOU KNOW THAT THE CAR IS DOING STRANGE AND WHEN IT HAPPENS(motor hot or cold)
. They can diagnose the problem area FASTER. The faster they do the correct repair, the cheaper it is for you.

The question is, is the temperature rising those extra few degrees above what they used to so the fan comes on suggesting there may be something like a faulty water pump, sticky thermostat, blocked radiator, or a faulty thermo switch that turns the fan on. If the fan starts as soon as you turn the ignition on when the engine is cold then you have a stuck on thermo switch.
Farm vehicles can be bad for grass seeds or insects blocking the radiator core, but a city vehicle may have had a bit of rubbish fly up and be sucked against the radiator. Check the radiator and air conditioner condenser in front of it for any blockages slowing or lowering the air flow through the radiator which would cause the temperature to rise enough to trigger the fan to come on.

One hundred ninety eight (190 degrees) is not that hot and suggests the cooling system is working as designed.
The lower hose is lower because that is where the coolant is coolest. The upper hose gets hot because that is where the hot water leaves the engine.
Make sure the system is toped off and the recovery tank is at the proper level.
While the fans do go bad- if they are still working there's no need to replace them yet.
Cars differ- some cars the fans will turn off if the ignition switch is turned off, on others they will continue to run for a short period of time and yet on others till the switch says the engine in cooled off. On most cars with electric fans- if the AC is on the fans are on.

Get a $20 IR digital therm gun and check the thermostat housing temp, the radiator fan switch is usually mounted on there.
Now check the fan thermostatic control switch to see if it a constant short to the chassis ground when the engine is cold.
This is usually an inexpensive part to source, about $25 and some work to get at it with a large deep well socket to replace.
After finding the TC switch, disconnect it with the engine off, then start the car. If the SW was shorted out, the fan won't run.
If the fan still runs constantly, you may have a bad fan relay with welded contacts. Find the relay and remove it to check it.

If the upper hose is hard, so is the lower hose. The cooling system has a 15 PSI pressure cap on it. The lower hose should be
cooler then the upper radiator inlet, that means the radiator is working properly. Check the cooling fan con switch first off here.

Your car would set a PO code flag if you had a stuck thermostat, again, the reason to get a $20 IR digital therm gun to know!
Do the testing with the A/C OFF! The A/C will activate the radiator cooling fan constantly while the A/C compressor is running.