According to Jaguar 2007 XK/XKR specifications the coolant thermostat begins to open at 190F (87C) and becomes fully open at 203F (95C). The 2010 and later models, with direct injection, may have a different thermostat, which I am unable to confirm.

I don't feel that an operating temperature of 203F is optimum for power and economy.
A lower temp around 185F (85C) is better at reducing detonation, which results in better power/economy. This applies to not only to NA motors but also to supercharged motors.

My reference source is A. Graham Bell, a Brit who now lives in Australia. Bell is a consummate tuner and has written several books, all of which are very readable. In his latest "Four Stroke Performance Tuning" at page 575 he writes:

"A high-temperature thermostat, which maintains the water temperature at 88-90C is usually fitted to production cars, but that is not the temperature for best power. The 88C thermostat is fine if you want good heater efficiency in winter, and the higher temperature partly compensates for the stock manifold and carburetor being unable to vaporize the fuel properly, but apart from that there is no reason for its use.

Some feel that high engine coolant temperature in the range of 90-100C is good for power. The theory is that anything lower just takes away heat energy, which we should be using to push the pistons down and produce more hp. To an extent this is true at low engine speeds and small throttle opening, but generally in a full-throttle, high-rpm dyno test an engine will make more power at coolant temperatures in the 70-80C range. Only dyno testing will confirm what is ideal for a particular engine, but in my experience I rarely see an engine that makes more power running higher than 84C or less than 68C. I have seen engines gain 2-3% more hp when the temperature was dropped from 90C to 70C; conversely I have seen gains when the temperature was pushed up from 65C to 80C."

My experiment was to find an aftermarket 180F (82C) thermostat that fits the Jaguar motor. In 2007 Jaguar went to a smaller diameter thermostat that is held in place in the black plastic thermostat housing by means of a small bridge-type bracket the is fitted into slots in the housing. Jaguar sells the housing complete with thermostat for well over $100. Far cheaper is the thermostat itself under part number "1 x AJ811788". This part comes disassembled; and is made in Germany.

I took my OEM thermostat to my local NAPA store to see if they could duplicate it in a lower temperature. NAPA has a #166 thermostat rated at 180F/82C. It sells for just $11.99. To install this NAPA thermostat requires using the locking bridge bracket from the OEM thermostat. Then the NAPA spring retention mechanism is redundant and can be cut out/discarded.

I won't get into the procedure to R&R a thermostat other than to say it is fairly easy on the NA motor.

The result is that my motor now runs in cruise at 184F/84C. It seems to get a bit better gas mileage on my 40 mile test run (flat freeway at 70mph). In stop and go driving temperature rises to over 200F(93C), but higher temperatures are limited/protected by the electric fan whose settings remain the same. I have not experience any real cold outside temperatures with this new thermostat. But, this is not my first experiment with cooler thermostats. With a 180F thermostat in another vehicle my heater functioned quite normally at minus 25F.

 

The hypothesis by A. Graham Bell sounds reasonable.

The gain might be from the ecm being able to avoid pulling advance due to the engine being slightly cooler.

It's too bad that the cooling system appears to be sized such that the temperature starts rising in low speed conditions.