Is'nt there a wire of some sort in these jags that you can ground out to clear system codes?

Get a workshop to run an ECU diagnostic as this might show where the fault is. Check the usual faults - thermostat, coolant level for leaks (cracked hoses, perforation in the radiator or leaking end tanks), fan fuses and relays and the condition of the radiator (no obstructions in the cooling fins, the core isn't blocked up with corrosion etc) and fan condition as they can burn out. Next place will be the thermo fan sender unit and any possible wire faults (damaged wiring, corroded connections, bad ground connections etc) If the car has never had a cooling system flush, now would be the time - and replace the coolant with a recommended product for your Jag.

Usually with a sensor, I check the sensor wiring circuits first, before replacing the sensor. Unplug the connector for coolant temp sensor, start the engine, check resistance across sensor terminals as engine warms up, that resistance should change, does it?
The two wire connector, one wire is ref voltage, I believe 5 volts. the other wire is ground, mainly black in color. That ground is shared by many circuits. One of the other circuits could be causing you a problem?
You could have air in the system from replacing sensor? I'm just thinking out loud.

the late 90 tahoes and trucks had a corrosion problem with their abs systems crud rust corrosion would get under the sensor and lift it back enough to cause problems such as low speed activation at under 5 mph or codes for all sorts of problems or just plane old short out ---try removing the sensor and clean mount (scrape lightly and put a anti corrosive on hub mount an clean around sensor

What is the fault code in the transmission control modules memory, if the light is on the code must be read with a special scan tool through the vehicles diagnostic service port.

If you go to a local autozone, they will scan/clear ODB2 codes on your vehicle for free.

the car you have is the jag x300 series the main probs with this car are the lambda sensors and/ or the catalysts and you will get high emissions. to help sort this out you need someone with ids or wds software to help to check the fault codes or monitor the live data the ign timing is controlled by the ecu lower rh A post! its not adjustable

Air intake temp sensor. Check the wiring to the sensor and make sure there are no bad places or hard kinks. If that doesn't change things replace the sensor.

I think you can buy a code reader from most any parts store for $40-60 and use it to find and reset the codes in your Jag. Good luck!

Friend, your situation could be taking place on ANY vehicle, not just the Jag. Anytime this type of thing happens, no matter what it happens to be, ALWAYS go directly to the ground. Check ALL your ground connections on every ground wire you can find, and the ones you can't find, under the dash that are held to the firewall and any metal braces by a simple little screw that could be loose. I find this stuff is a LOT like connecting a trailer to a vehicle for the lights. Sure it's wired properly, you know what your doing!!! Then you check and tighten the ground wires between the vehicle and trailer and it now works. ALWAYS go directly to the ground connections. That's normal procedure. If it still doesn't work, get out the test light and start checking for power. But then your not doing trailer lighting. Get yourself a wiring diagram and check it closely.

I have the same exact car and when I had to replace my battery I had to reset radio code also. Fortunately, I have the code card, but I didn't know that at first and I typed in a random code, and then it kind of "froze" it saying Searching for code or something to that sort. I called a Jag 800 number (any Jag 800 should be fine) and they told me the steps and my code, you will probably need a VIN #.