It's a "deep well" socket, and I seem to recall it being an "inch" size, rather than metric/ISO. I don't have a sensor handy, or I could tell you a size.
Since it's brass, use a 6-point socket, rather than a 12-point. Rounding it off would REALLY suck!
I'll give you this one for free - but I've covered it a few times in the last fortnight in posts and PMs...
Jack up the rear of the vehicle, until the rear end of the cylinder head is the highest point of the engine.
Loosen the sensor to "finger-tight."
Top off the "football" tank, and unscrew the sensor with your fingers. Leave it loose (topping off the "football" as needed) until you start to get coolant out past the sensor.
Tighten the sensor finger tight, and then an additional 1/2-turn or so with a wrench.
Lower the vehicle.
Check your coolant levels at intervals for the next week or so, and top off as necessary. If it's your daily driver, having the same coolant level for three days on the run is good enough to quit checking.
I find it helpful to put a strip of masking tape, vertically, on the side of the "football." Make a mark to where you top off the coolant, and use that to check the level. If you add, try to get it on or near that mark, to avoid confusion. You can pull the tape strip off when you're done.
Next time you open things up, you might want to search up my posts on "thermostat drilling" to make the system self-purging of air.
5-90
