Looking at the original question ..
(a) diesel and avtur are very similar fractions .. as I understand it, avtur functionally is diesel with a bit less oil (plus a lot more attention to refining QA)
(b) with reasonable fuel handling QA avtur shouldn't have too much trouble with water freezing, although that can and has been observed
(c) the fuel is a complex mix of hydrocarbons each with its own freezing point
(d) as the fuel temperature decreases, there comes a point where the highest component hydrocarbon starts to freeze (start of wax formation).
(e) for determining the freezing point in the lab, when (d) occurs, the fuel sample is allowed to warm up until there is no evidence of phase transition .. the temperature at which this occurs is the declared freezing point. Typical test procedures may be reviewed at ASTM D2386/D5901/5972.
(f) different fuels will have different declared freezing points (and will/should be declared in the specification data) but a typical ballpark is around -45C (for one spec with which I am familiar) although individual test samples may well show low freezing temperatures (eg looking at several test sample reports for this spec, the sample freezing temperatures were around -55C).
(g) for later design standard aircraft, the AFM should have some guidance regarding fuel temperature problems.
I have an Industry paper with gives a lot of background if you would like to read it .. around 2Mb file
I am not familiar with the particular STC but I would be VERY wary of using diesel .. in Australia, for instance, I am told that there is no definitive standard for automotive diesel ... I have been caught out a couple of times in my vehicle with "bad" batches of diesel. Using avtur, though, should avoid that sort of problem.
The concern raised by lusthansa ought not to be frowned upon ... just that problem can and has occured with VERY raised eyebrows the resulting pilot response ....