In the depths of the Internet, I noticed a version – the problem of cylinder No.6 is overheating of its injector.
My theoretical considerations ruled out such a possibility. But, to not limit everything with a theory, I took a thermal camera and performed a range of measurements.
I will start with the theoretical part.

Here, the B58 engine is shown without the decorative cover.
We can see ignition coils, on the right side of them, the “bits” of Rail.
Situation on the go.
As indicated by my thermal measurements of the ignition coils (here), on the go, there is an excellent air exchange below the decorative cover. Accordingly, we can not worry about the adverse effects of exhaust or any other external heat source.
Part of the injector nozzle is pressed into the engine block. The thermal contact of both parts is excellent. Accordingly, the injector could overheat if, for example, the engine block is overheating. Unfortunately, this idea should be abandoned, because significant local overheating for these engines is not observed (and is not even possible – then the engine block/”head” would “twist”; the coolant would turn into a gas, destroying some of the plastic connections in the cooling system, etc.).
The top part of the injector is pressed into the Rail. Both parts are made of metal, and their thermal contact is also excellent. Even if there were some heat sources that would heat up the Rail (but there are none), all injectors of a particular bank would be heated up.
The situation in idle.
I think that we can dismiss the idea of local overheating of the engine block – in idle, the total radiated heat output of the engine is only several kW, most of which is actively cooled via the cooling system. There is nothing to heat the Rail too.
Possible cause of heating – heating, coming from the exhaust, which is not drained exactly during idle. Precisely in these conditions, the ignition coil of the 6th cylinder is overheated (the measurements confirm it – temperature of the body of the ignition coil rises for 40 .. 50 °C, reaching 90 .. 95 °C during 20 .. 30 minutes and continues to increase).
I have several objections to the theoretical part, which reduce such a possibility to a minimum:
a. As we see, the ignition coil is in the “front” of the injector – it excellently blocks the hot air flow, the injector is “hiding” lower/deeper – as we know, hot air rises;
b. both the nozzle and the inlet part of the injectors are thermally “stabilized” (cooled/heated, depending on the situation);
c. The injectors have a small surface area, which reduces the impact of the hot air flow even more.
Theory is theory. I’m taking my thermal camera and watching the actual situation.

Here, the image is after quite dynamic driving. The brightest fragment in the top left part of the image above: the engine block. Yes, its corner has heated more. But the difference with other, better cooled spaces is only several degrees.

Here is the image after 15 minutes of idle time. As we see, the ignition coils of the last cylinders are becoming “brighter” – they are heated by the exhaust system (mostly: CO catalytic converter). The temperature of the engine block is very even. Behind the ignition coils, we do not see any heating parts – the temperature of all elements (Rail, injectors) is similar.
Unfortunately (or rather – fortunately), I did not manage to confirm the overheating of the injector of the 6th cylinder (more precisely – it is heating more than the injectors of other cylinders). Neither running nor idling.
