I can wait until spring; hot turbo's are not really my problem at this time of year. Here's something to ponder during your time off.
We both (presumably) have similar trucks; 2006 Dmax's. My owners manual has some great info in it. One of my favorite features is the cold weather "high idle" feature that warms up the truck. I have a low level work truck; it's not a fancy truck (like an LTZ, etc), so I don't have the DIC steering wheel controls. When I have to reset my oil or fuel filter info, I have to tap dance on the pedals (most people tab through with the DIC steering wheel controls). But my point is this; I can turn on/off the warm-up feature with my pedals because there is a specific reference in my owner's manual as how to do this. It is well described, and well documented in print. So follow along ...
You claim that your STOCK Dmax trucks (you indicated you have more than one) all have this "cool down" timer feature, and your trucks are also 2006 models, just like mine. But NOWHERE in the owners manual can I find any reference to a cool down timer feature. One would think that if a vehicle were going to run AFTER the driver removed the key, GM would have put SOMETHING in print as to why and how that happens. After all, don't you think that might scare a few people that were not expecting a vehicle to continue to run AFTER they removed the key? So, at the very least, if ALL Dmax trucks do this, as you inferred in your original statement, don't you think there would be some mention of it in the owners manual?
Further, if your trucks do it, and mine does not, (and presuming your trucks are factory stock), that would mean that somehow the feature is able to be turned on/off, would it not? Again, don't you think they would have put SOMETHING, ANYTING in the manual as to the procedure to turn it on/off, just like the cold temp high-idle feature?
Also, after checking with public posts over the last day on a few different GM truck forums, I cannot find anyone that contends that such as feature is STOCK on all Dmax trucks. The closest I've come is a guy that says he can do it by manipulating his key-fob remote. Key fobs are NOT always factory stock! My base level truck did not come with key fobs; I have plain ol' keys. So at the very least, even if it were included somehow with the factory key fob, you'd STILL have to believe that GM would describe the function in the manaul, would you not? Well, not in my 2006 manual they don't, anyway.
What I think is that either you have some type of dealer installed GM accessory system, or other aftermarket remote start feature, or your just flat pulling my leg.
Again, I'd like to be wrong and have you be right, because that would mean I would also have the benefit of such a system. But right now, I don't see the evidence pointing that way.
So to come full circle, back to the poor OP and his oil topic, hot turbo temps might be an issue, and his lube choice might be mitigated by this at some point in his consideration. At the very least, if HIS truck does shut down upon immediate removal of the key (like mine does), then he should be aware of this so that he performs a "manaul" cool down event if warranted, like everyone else but daman.